Left Tackle - Unless you believe Will Beatty will fully recover from the broken leg that ended his 2013 season and then is able to come back and play at a higher level, this is glaring need numero uno. Their best bet is to use their first round pick on a turnkey solution such as Michigan's Taylor Lewan. The only other option would be to flip-flop Beatty with RT Justin Pugh, but that creates other issues.
Tight End - Do the Giants still believe Adrien Robinson is still the JPP of tight ends? Probably not as much as they did when they drafted him. Well, like it or not, he's still in their plans but they need to see him in extended action. That's something that can't happen until training camp. So, they need another TE from somewhere. Jermichael Finley has yet to be medically cleared and the other free agent options are not very enticing. That leaves the draft. They have met with NC's Eric Ebron, but unless they plan on using their first rounder on him, he's not an option, either. Someone may fall to them in rounds two or three, they hope.
Center - The Giants have a mixed past when it comes to free agent centers. Shaun O'Hara was a hit. David Baas was a miss. There are some free agent options available, but it looks like they responded already by signing JD Walton. If he can return to form after missing a season and a half, the Giants will have a major coup on their hands. If not, they may have to rely on Dallas Reynolds, bring back Jim Cordle and hope for the best.
Defensive Tackle - Currently, the Giants have only three: Cullen Jenkins, Markus Kuhn and Jonathan Hankins. A quick call to Mike Patterson would make four, but a year after fixing this unit, it looks like they'll need to bring in another body here.
Defensive End - Again, only three players here: JPP, Mathias Kiwanuka and Damontre Moore. JPP is still sealing with his back and shoulder. Kiwi hasn't panned out as well as the team had hoped. Moore is still largely unproven. Kendrick Adams, a UDFA out of LSU is also on the roster, but the Giants are his fifth team in two years. The solution could come from the draft or an inexpensive free agent signing. The Giants rotate religiously on the d-line, so a veteran specialist could fill this role. They looked at Anthony Spencer already and passed. They'll keep looking.