First of all, I own a $25 beater bike that I picked up from a garage sale a few months ago. It's an old(er) Univega Alpina Pro with wide (not sure if you'd call them mtb) tires. It's mainly for riding to campus (<1 mile away) and getting around town (not more than a couple miles).
I'd like to become a stronger rider, but am discouraged from taking longer rides because of the tires (I read in another thread not to regularly exceed 5 miles on mtb tires). Traffic is also kinda crazy in Berkeley.
Would I reap any benefits from using a stationary bike (the nearby dorms have a small workout room I can access for free)? Should I just try to ride (stationary) as long as possible? Other suggestions?