There are plenty of lists of "best available prospects," but this is a list I've made based on not only Dolphins' specific needs but also based on players the Dolphins had been linked to in the pre-draft process.
In my "Miami Dolphins Round 1 Leak/Smokescreen Summary" article, I noted how Ja'Wuan James was one of 30 prospects the Dolphins had brought in for a pre-draft visit. Not entirely coincidentally, James ended up as the Dolphins' first round pick, and GM Dennis Hickey mentioned specifically how seeing him up close at the Dolphins' practice facilities and getting a chance to have him work one-on-one with our offensive line coach John Benton helped sell James as a first round choice for the Dolphins while most experts had him as a 2nd round choice.
Therefore, any players the Dolphins brought in for a visit would are considered potential priority targets in the next 2 rounds, though the team could still draft a player they didn't have a chance to see up close. Likewise, Hickey talked pre-draft about how important "character" is when they're evaluating prospects, and perhaps unsurprisingly, all of the Dolphins' draft picks so far are team captains (3 for 3), so players who are team captains will be highlighted.
The Probables
Linebacker
The Miami Herald's Barry Jackson AND Armando Salguero each report that they've been told that the Dolphins are hoping to add a starting guard in the draft. If the Dolphins do that, then 2013 3rd rounder Dallas Thomas and 2014 free agent acquisition Shelley Smith would be in a competition to start at the opposite guard spot.
In my opinion, this is a draft that is deeper at offensive tackle than at guard, so if Hickey felt compelled to take Ja'Wuan James in round 1, it wouldn't shock me at all if offensive guard was our first pick in the second day. Names to watch?
Joel Bitonio is the guy that the Miami Herald's beat reporters say they each keep hearing. Several teams are thought to view him as a better guard prospect than tackle prospect, and the Dolphins are allegedly one of them. To quote Salguero:
"The Dolphins absolutely love, love, love Nevada tackle Joel Bitonio, a source familiar with Miami's thinking tells me. The team loves Bitonio as a guard and likely as a left guard."
That's pretty unambiguous. Jackson meanwhile says that he's heard the Dolphins like Stanford’s David Yankey, LSU’s Trai Turner, UCLA’s Xavier Su’a-Filo, Clemson’s Brandon Thomas (has a torn ACL), and Nebraska’s Spencer Long. Of those prospects, only Long had a pre-draft visit, and he's a TEAM CAPTAIN/HIGH CHARACTER guy (sound the alarm bells!), while Thomas was offered an invite before he tore his ACL and cancelled his remaining visits.
Also, to my knowledge, there are no rumors connecting Marcus Martin out of USC to the Miami Dolphins, but he's a guy to watch in round 2 because of his significant experience at both guard and center. Current Dolphins center Mike Pouncey's punishment stemming from the bullying scandal still hasn't been finalized, so the thought of addressing both guard and backup center with 1 draft pick could prove tempting to Hickey.
UPDATE: Armando Salguero just updated his blog, and he says he was told by a source that the Dolphins think highly of Marcus Martin. The source also says that in addition to OG, they'd like to get a WR to challenge Rishard Matthews.
Linebacker
The Dolphins were interested in CJ Mosely and VERY interested in Ryan Shazier, but both linebackers were picked before #19 in the first round.
Starting in round 2, players including Chris Borland of Wisconsin and Shayne Skov of Stanford come into play, though neither has visited the Dolphins. Names that have been connected to the Dolphins through either visits or known meetings with coaches include Preston Brown out of Louisville and Jordan Tripp out of Montana (both are more of round 3 to 5 selections than round 2, though).
Wide receiver
Wide receiver is arguably less of a need than linebacker or guard, but wide receiver should be viewed as a potential round 2 to 3 pick due to the strength of the WR class and the fact that our GM is ostensibly committed to picking the best player available.
Marquise Lee out of USC is arguably the best player remaining, regardless of position, and he earned a pre-draft visit with the Dolphins. The other projected early round receivers getting a visit to the Dolphins are Odell Beckham, Jr, who was drafted in round 1 by the New York Giants, the still available Martavis Bryant out of Clemson, and the still available Donte Moncrief out of Mississippi.
Other receivers available who would make sense as picks in either round 2 or 3 include Jordan Matthews out of Vanderbuilt, Allen Robinson of Penn State, Davante Adams of Fresno State, Cody Latimer of Indiana, Josh Huff out of Oregon, and Jarvis Landry out of LSU.
That's a long list of receivers who could potentially be the best player available on Hickey's draft board in either round 2 or 3, so if he really is following his draft board and drafting based primarily on talent, we could be hearing one of those names today.
The Maybes
Tight end
Barry Jackson of the Miami Herald reports that some coaches have doubts about Michael Egnew's ability to develop into a consistent receiving threat, and Dion Sims has been primarily used as a blocker both in college and as a rookie in the NFL. Jace Amaro out of Texas Tech, Troy Niklas out of Notre Dame, and Austin Seferian-Jenkins are the top 3 TEs remaining, and ASJ in particular was the only one to have a pre-draft visit with the Dolphins.
Safety
The Dolphins are allegedly looking at potential backups and special teams contributors who are expected to be day 3 and/or undrafted free agents, per Jackson. Dion Bailey out of USC and Ed Reynolds out of Stanford are probably the best safeties left, but neither have been connected to the Dolphins.
Cornerback
The Dolphins are interested in a cornerback to challenge Will Davis for snaps as dime cornerback. Names connected to the Dolphins who are potential day 2 selections include Phillip Gaines out of Rice and Liberty's Walt Aikens.
Dark horses
Running back
Not a single running back was drafted in round 1 this year, and the Dolphins didn't use any of their pre-draft visits on running backs. The position has become increasingly devalued as more teams pass the ball predominantly and use a deep rotation at running back rather than relying on 1 elite talent. Best running backs expected to be drafted today include Jeremy Hill out of LSU, Carlos Hyde out of Ohio State, Bishop Sankey out of Washington, and Tre Mason out of Auburn.
Defensive Tackle
The Dolphins didn't use any of their pre-draft visits on defensive tackles, and the Dolphins didn't attempt to draft players like Ra'Shede Hageman of Minnesota and Louis Nix of Notre Dame as they fell in the draft, suggesting that they're not overly interesting in adding defensive tackle talent to a rotation that already features 3 starting caliber defensive tackles in Jared Odrick, Earl Mitchell, and former Pro Bowler Randy Starks.
Defensive End
Mel Kiper of ESPN actually listed defensive end as one of the Dolphins' top 4 needs, but the Dolphins' defensive end rotation already features a multiple Pro Bowler in Cameron Wake, a sophomore former 3rd rounder who had 11.5 sacks last year in Olivier Vernon, a former 3rd overall pick whom the coaches vow to give more snaps this year in Dion Jordan, and a former UDFA whom the coaches love due to his fundamentally sound play against the run in Derrick Shelby. Round 2 or 3 is simply too early for a defensive end, especially since this isn't an especially strong class for 4-3 DEs.
Defensive end, cheerleader, long snapper, and punter are the Dolphins' 4 undisputed positions of strength.
That being said, the Dolphins are reportedly interested in a few prospects that are day 3 selections or UDFAs.
Offensive Tackle/Guard
Nope, I'm not kidding. There are several solid to good offensive tackle prospects available including Morgan Moses, Cyrus Kouandijo (who like Ja'Wuan James had a pre-draft visit with Miami), Jack Mewhort, Michael Schofield, and Billy Turner (cue cursing by the folks who wanted a round 2-3 OT). Combine that with the fact that some draft experts including Mike Mayock believe Ja'Wuan James can play guard, and offensive tackle remains a potential (though unlikely) draft pick.
In particular, the Dolphins have been connected to Virginia tackle Morgan Moses. According to Armando Salguero, Dolphins offensive coordinator Bill Lazor has strongly advocated in favor of Moses due to having coached Moses back when Lazor worked at the University of Virginia. Meanwhile, Barry Jackson says Michigan tackle Michael Schofield was told by the Dolphins that they like him a lot. So Moses and Alabama's Kouandijo in round 2 and Schofield in round 3 in particular are OTs to watch.
So if one those OTs happens to be the best player available when the Dolphins pick, it's entirely possible that the Dolphins draft another offensive tackle, and the coaches have two rookies battle over who starts at guard versus at offensive tackle. Ja'Wuan James would be favored over any round 2 or round 3 rookie in this scenario because James was drafted in round 1, suggesting the Dolphins' view him as the best OT talent available at the time. However, a guy like Moses perhaps could be asked to mostly play left guard but slide out to left tackle in case of a Branden Albert injury and perhaps even be Albert's successor down the line.
Look, I'm not advocating for this strategy. I'm just pointing out that it is absolutely a viable one for the Dolphins to follow, hence it being a "dark horse" day 2 pick. Personally, I'm a big fan of veteran offensive tackle (and UMiami alum) Jason Fox, who was signed by Hickey in free agency and has flashed starting potential both in training camp with the Detroit Lions and when given regular season snaps, so I don't see the value in drafting another OT. However, the Dolphins' continued interest in drafting offensive linemen suggest they're not optimistic that Fox could hold up as a 16-game starter.
Quarterback
The Packers drafted Brian Brohm in round 2 and Matt Flynn in round 6 to serve as backups to Aaron Rodgers, so a round 2-3 pick at QB to be a backup wouldn't be unreasonable, though it is unlikely. Names to watch on Day 2 include Derek Carr, Jimmy Garoppolo, and Tom Savage, who are generally considered the best quarterbacks remaining. In terms of QBs the Dolphins have reached out to, though, Zach Mettenberger and Aaron Murray are the only two who have a shot at being picked on day 2. The rest are day 3/UDFA prospects like Stephen Morris, suggesting the Dolphins are looking for potential backups, not starters (Sorry, Omar Kelly).