I have been working out who might be available where and how they fit into the Giants scheme:
Quarterback- Eli Manning is 36 years old and the team has started discussing finding his successor. Eli had a down year last season, but a good deal of his issues could be attributed to a weak offensive line, a lack of a proper running game and a stable of relatively short WRs. The team seems to have fixed some of the issues. The team could seriously consider someone like Mahomes in round one (assuming he lasts and there isn't an early QB frenzy). The team really doesn't have the juice to move up significantly should there be a run (their 3 round pick would only buy them 4 spots). They could "settle" on lower round QBs. Jaws thinks that Pitt's Nathan Peterman would be a good fit for the Giants and should be available in the 3rd round. There is also Miami's Brad Kaaya who should be around rnds 4 or 5 and while I was less than impressed does have good traits for Ben's offense. If things don't work out in terms of the way the draft plays out, I see the team staying pat as Geno Smith gives them some flexibility.
Wide Receiver- I would be shocked if the team drafts one as they are pretty settled at this position with the signing of Marshall
Tight End- The team now has a good blocker in Ellison, a TE they believe is a developmental guy in Adams and a guy who regressed (and doesn't block) in Tye. I see the team having room for a good TE. Njoku would be a nice option in round 1 (should he fall). Gerald Everett would be an option in the 2nd round. Bucky Hodges an option in the 3rd and Toledo's Michael Roberts a 4th round possibility. The team could stand pat at TE if need be (if the draft doesnt' fall or they need the picks for other players)
Running Back- This seems like a stronger but not desperate need. I think Paul Perkins will be the team's main back and Vereen offers a third down, alternate. There is also Darkwa and the newly signed Shaun Draughn. If the team does feel the need, I know many are high on Christian McCaffrey should he fall to the team in the first round. I am not seeing this though. If he were still there in the 2nd, I would have to think that Joe Mixon would be tempting for the team (but they may pass). Kareem Hunt would be an interesting option in the 3rd round and Chris Carson a 4th round possibility. I think odds are the Giants will draft a running back from the guys I mentoned, but it's far from a sure thing.
Offensive Tackle- While I have been one calling for a new LT, I can't help but shake the feeling the Giants will stand pat with Flowers at LT (I think the Fluker comments along with the comments of the ownership and coach is why). If the Giants want a plug and play LT I suspect that the options in round one (the only round I see potential starters) is Ramczyk, Bolles and Dawkins. It's possible at least the first 2 will be gone when the Giants draft and I am not sure how they feel about Dawkins. After that you are looking at developmental type prospects such as Taylor Morton (RT only) in the 2nd, Roderick Johnson in the 2nd, Jermaine Eluemunor in the 3rd, Julie'n Davenport in the 3rd or Antonio Garcia in the 3rd (maybe the 2nd). I see the Giants drafting a starter in round one or at least one of the projects I mentioned.
Offensive Guard/Center- At first glance, this position would seem to be solid with Richburg at center Pugh, Jerry and Hart/Fluker (the loser of the RT competition) and Jones the backup guard/center. However, Pugh and Richburg are both free agents next year and the team's cap will be tighter next season. So there could be room to draft a guard or a guard who can double at center. There are plenty of interesting prospects to pick from. In the 2nd round, you have Dan Feeney and Taylor Morton (G/RT). In round 3 you have Nico Siragusa and Dorian Johnson. In the 4th you have Isaac Asiata and Damien Mama. I see a guard being drafted as a possibility, but not a really good one.
Defensive End- With JPP signed the odds seem unlikely that the Giants will take another DE in Round one or maybe two. Now JPP and Vernon were overworked last season. The real question is if one of the trio of Wynn (tendered), Odiggy or Romeo O. Romeo is still developing and should be better this upcoming season. Odiggy has been hampere by injury and there is little to believe he will be able to stay healthy and Wynn is a run stopper who regressed in his sophomore season. Daeshon Hall in the 2nd round and Hunter Dimick in the 3rd round looked to be interesting prospects.
Defensive Tech- This will be tricky until the Hankins situation is resolved. If Hankins signs the Giants long term offer there will be no in interest in a 3 tech DT. If he signs a one year deal or the Giants are forced to sign an older vet than there could be players of interest in the draft. Chris Wormley DE/DT would be high on my list if he makes it to the 2nd round spot (might even trade up). Montravius Adams is another option in round 2. In round 3 options would include (or might include) Larry Ogunjobi or Eddie Vanderdoes. In round 4 you would have to consider Jarron Jones and round 5 Dalvin Tomlinson. I see little need for the Giants to draft a 1 tech with Snacks and Thomas. Bromley remains the backup 3 tech.
Linebacker- The team could skip this position with the core of Kennard (who is a free agent after this season), Casillas, Goodson and Robinson. That group can get the job done. The team does have some backups as well in Herzlich, Thomas, Skinner and Pinkins. If the team were to draft anyone I think it would be a MLB or a hybrid pass rusher LB to play a sort of Kiwi role. Zach Cunningham would be the sort of similar to Kiwi type to draft in round 1. Ruben Foster would be a huge impact MLB who may drop to the Giants at 23. Beyond that I see little to interest the team other than maybe Richie Brown a MLB who would be a nice 5th round pick.
Cornerback- You would think with Jenkins, Apple and DRC there would be little need to draft a CB. However this draft class is full of CB prospects and the team needs another solid option to eventually replace DRC (who I see the team parting ways with after this season). I see CB as likely anywhere after round one. In the second round Fabian Moreau would be a nice choice. Round 3 you would have option like Shaquill Griffin. 5th round would offer Brian Allen and Brendan Langley. There are others but I stayed away from the zone type CBs as the Giants play more M2M.
Safety- The team seems pretty solid at this position with Collins and Thompson set to start. Adams is a nice backup along with Berhe. There is also veteran Rahim Moore trying to make a comeback. If the team drafts a S, I would expect it to be very late in the draft. The team also has former draft pick Mykkelle Thompson.