Should I change PhD programs based on available recreational activities?
Go for it!  Many east coast academics, or people in general even, are not going to understand how you feel.  In my experience, for many academics on the east coat, outdoor recreation is not a priority (yeah, yeah, it's a generalization...).

You say:


  "either of those places offer me a refuge to break the work-sleep
  cycle (I am obsessed with backpacking and climbing). At my current
  institution, I feel very "trapped", like there is nothing here except
  working, sleeping, and drinking"


100% agree.  You can find a way to make grad school and your outdoor passions work together.  Just don't expect many of your (east coast) colleagues to understand this.  I have found that many academics in the west are very understanding of the outdoor lifestyle.  I've worked with researchers who live out here because of the outdoor opportunities.  The point is that sharing your honest reasons for wanting to transfer may actually help build connections.

I need to be near, or on, mountains.  This is a huge factor in what makes me happy.  I grew up in the West, but my undergrad and graduate pursuits were on the East coast because I chose to go to schools with name recognition over location.  For undergrad it was okay, but I couldn't stand it in grad school.  I turned down some great opportunities on the East coast to move back to the West.  Most of my advisors could not understand why.  Only one who loves to ski actually supported me.

As for how this will play out in industry, this is hard to say.  I am currently in industry in an area with tons of biking, climbing, skiing...  Part of the company culture is being outdoorsy, fit, and adventurous.  While the name of my school played some role in getting an interview, I think what really made me appealing was that I could connect with my future boss about all the awesome things we do.  Now I have a beard, long hair, and go on road trips all summer.  Wouldn't be doing any of that out east.