here's a couple to start with:
"MTR" (Mavalli Tiffin Room). Go for breakfast. A Bangalore tradition, landmark building, and utterly delightful experience. Not to mention spectacular food. Try the masala dosa's and rawa idly's, be sure to dip / drizzle both with the ghee. Pick up sweets at the MTR sweetshop next door -- heavenly Mysore Pak and Tirupati laddoos.
Empire Hotel -- lots of branches. Real "down-home" Bangalore experience. My favorites there include the butter chicken, gobi manchurian (dry), spit-roasted chicken, coin perota's (small pancake-size flakey breads), and excellent shawarma.
Karavali, Taj Gateway Hotel -- Malabar cuisine (Goa, Kerala, Coastal Karnataka). Fabulous seafood from India's west coast, with spectacular appam's (pancake-like breads, flaky and soft at the same time -- amazing) cooked to order by a chef in the dining room). Excellent place to try pan for the uninitiated as well (fresh betel-paste post-meal digestive).
Am in a rush, here are some other excellent picks:
Hyderabad Biryani. Just what the name says. Great.
and when you want to go western, Olive Beach is quite good, and Sunny's is also very popular and has a great deli section at the back for fresh cheeses, hams, etc. (you can get this at olive beach as well.)
I'll think of others, am a foodie that's been living / eating in Bangers for 4 yrs now
oh, and also try Chandni Chowk in Koramanga, fun atmosphere and decent North Indian food.