Just looking at available UFA and sort of compiling a list of maybes. I'm mainly using guestimates as to how I think we could afford, how productive I think they might be, and they're age.
First Depth Chart (order listed doesn't reflect anything):
Center
Eriksson Ek
Rask
Sturm
Dewar
Rossi(?)
Right Wing
Zuccarello
Fiala
Foligno
Bjugstad
Left Wing
Kaprisov
Greenway
Boldy(?)
Left Defense
Brodin
Soucy(?)
Right Defense
Spurgeon
Dumba
Addison (?)
Goalie
Talbot
Kahkonen
Given the depth chart listed above. We have a few positions that could use bolstering or filling; center, left wing, and defense.
Centers
Krejci
Stastny
Wennberg
Bonino
Haula
Zajac
Bozak
Right Wing
Hudson Fasching - What happened to him? Might be a decent player to take a chance on. Probably high risk/medium reward. Should come fairly cheap though. Might be a decent 13th forward?
Left Wing
Tyrell Goulbourne - Mostly a depth/4th line signing
Nitika Gusev - Maybe as a 3rd liner?
Left Defense
Ian Cole - Assuming he takes a paycut
Jamie Oleksiak - Decent defender which would give us more size
Jake McCabe - Coming off an injury but was a pretty decent defender
Cody Ceci - Eh lol
Jack Johnson -
Right Defense
Zach Bogosian - Not sure how I feel about this. Really just a depth signing
Luke Schenn - Depth signing
Edit: Realized I didn't do Goalies
Goalies
Jaroslav Halak - Could be a decent #1 if Talbot is taken and a good tandem if Kahk is taken.
Petr Mrazek - Similar to Halak, but more towards a backup
Linus Ullmark - Similar to two above
Feel free to submit your own ideas and thoughts, and to rip this to shreds.