I think that Braun is our best moveable piece right now so it's best to look for a hockey trade.
Teams that could use Braun-forwards I would want for him (my thoughts on the trade)
Arizona Coyotes-Dylan Strome (highly doubt they do this)
Buffalo Sabres-Jeff Skinner/Sam Reinhart (doubt they do either of these)
Toronto-Marleau/Kapanen/Kadri (probably would do/might do/won't do)
Columbus-Anderson/Jenner (might do/probably won't do)
Philadelphia-Simmonds (probably works the best)
Pittsburgh-Hagelin/Rust (might do/might do)
So out of all the teams that might be able to use Braun the only teams that have a forward that works for us (at least IMO) are Toronto, Columbus, Philadelphia, and Pittsburgh. I think that Marleau has too big of a cap hit and Kapanen isn't proven enough without a huge plus. I don't know if Columbus will want to give up either of Anderson or Jenner when they have Jones and Savard on the right even though Braun is an upgrade on Savard. Pittsburgh I think that Hagelin is too expensive, I would love Rust though, I just don't know if we can make the cap work here.
This is the trade I'm proposing based around Simmonds and Braun:
Simmonds (1 year left at 3.975)+Hagg (2 years left at 1.15 RFA) for Braun (2 years left at 3.8)+Karlsson (2 years left at 2M)
We save a little bit of cap space and get a good power forward. We also get a replacement for Braun.
Lines after this trade:
Kane-Pavelski-Donskoi/Labanc
Hertl-Couture-Meier
Simmonds-Thornton-Labanc/Donskoi
Sorenson-Suomela-Goodrow
Chartier
Vlasic-Karlsson
Ryan-Burns
Hagg-Dillon
Heed, Simek