Looking for good cheap eats within walking distance of Back Bay station
Within walking distance is Picco, a South End thin-crust pizza restaurant with a good beer selection and homemade ice cream. There were recent postings raving about their calzones. Also nearby is Addis Red Sea, an Ethopian restaurant I have been meaning to revisit after a few years. I wouldn't call either restaurant cheap but I would certainly not call them expensive.
You can also go to Laurel, which is an attractive space with standard American (comfort)food. It may be a little above your price range.
Red Sea Cafe
1127 Harrison Ave, Roxbury, MA 02119
b.good does not serve alcohol.
Nearby places that qualify as a night out destination include Coda on Columbus Ave. near Dartmouth. It has good food and reasonable prices. Also in the area is Six Burner on Dartmouth across from Back Bay Station. This place is new (same owners ran the previous plave called Firefly) and I have not tried it yet.
329 Columbus Ave, Boston, MA 02116
130 Dartmouth St, Boston, MA 02116