This year, their greatest need is at linebacker, mostly inside but outside too, followed by their defensive line. They could use another cornerback. What these positions have in common is that they've lost starters at them (CB Casey Hayward, NT B.J. Raji, LBs Nate Palmer and Mike Neal) and they will be missing players to suspension (DT Mike Pennel, B Demetri Goodson). Another position that could use some more depth is their offensive line, where injuries were a major problem last season and Don Barclay and JC Tretter both showed their limitations, though its unlikely they'd use another high draft choice on either an offensive lineman or defensive back.
The problem at linebacker is that after Alabama's ILB Reggie Ragland (who should be long gone by the time the Packers are on the clock), the draft is very thin at inside linebacker. While selecting an outside linebacker in the 1st round would hardly be a wasted selection, it would probably prevent them from moving LB Clay Matthews back outside, so it doesn't seem like an outside backer would be their preference.
They might even consider trading down, if the mock drafts are true that the Packers are interested in a defensive lineman, because that's a deep position in the draft and they could probably get a quality DT anywhere in the 2nd round. A couple of quarterback needy teams might be looking to trade into the late 1st round:
If they do find themselves with multiple 2nd round picks (after trading out of the 1st round), in addition to drafting a defensive lineman, they might also consider selecting another wide receiver. While WR Jordy Nelson is back and they have a number of young receiving options already, most of their young wide receivers played poorly last season. WR Davante Adams was pretty much a disaster last season and things weren't much better for either WR Jeff Janis or WR Jared Abbrederis, who both showed promise but also received negative DYAR ratings from Football Outsiders. It's very rare to have one of Aaron Rodgers's receivers score a negative DYAR, and it was the first time that three of them did it in a single season. If a receiver has a high draft grade and he's available in the 2nd round, I'd have to think they'd seriously consider it.ICYMI, Broncos and Browns rumored to be moving up from 31, 32. #Packers a likely target - https://t.co/U3dxjVSQ0f— Walter Cherepinsky (@walterfootball) April 25, 2016
It's also a deep position with 10 wide receivers currently ranked in the Top 80 players according to CBS Sports (all 1st or 2nd round grades). One interesting receiver is Oklahoma's Sterling Shepard, because of his "quickness and balance to change directions in a flash" along with his good hands. If he was 6-2, 220 lbs. he'd probably be talked about as a Top 10 pick, but at 5-10, 194 lbs. he's about the same size as WR Randall Cobb and he'll probably be drafted in about the same spot (late 2nd round). The Packers need help on defense but they have to make sure the offense is better next season too.