Depending on how you define "meal" and "Buffalo" (as in downtown, city limits, etc), but there's lots of good eating to be found for $10 or less. These are just a couple affordable spots I could think of off the top of my head:
Amaryllis, Delaware and North, Buffalo: upscale, polished restaurant with very pricey food BUT you can sit at the beautiful bar and order an amazing $8 sandwich (or a $15 hangar steak) from their bar menu. Probably the "best" meal under $10 I can think of...in a place where meals are normally $20 and up.
Quaker Bonnet, Allen St., Buffalo: homemade comfort foods, like chicken pot pies and meatloaf, plus a rotating list of specialties and outstanding desserts - all are pretty cheap, but portions can be sizable.
Betty's, Virginia St., Buffalo: has good sandwiches served with side salads for under $10 at dinner, but much more under $10 offerings at lunch.
Sterling Tavern, Hertel and Sterling Place, North Buffalo: huge fresh fish fry with tons of sides for maybe $8? And good beer on tap.
Kentucky Greg's BBQ, George Urban Blvd, Depew: solid BBQ, good side dishes. You can get a filling meal here for under $10.
Schwabl's, Center Rd. near Union, West Seneca: excellent beef on 'weck with side of beets and german potato salad will run you about $8.95. During winter, you can add a Tom and Jerry, though you'll be just over your $10 limit.