Can anyone tell me what to do there (not to be missed) and where one might stay for a reasonable amount, not to far from city center. Am planning a trip there in early Feb.
Thank you.

The Zoo!

Coronado and the Hotel Del.

I haven't stayed there in awhile so I'll pass on the hotel advice. I like the Zoo, Balboa Park (check out the pipe organ concerts if you are there on a Sunday) and walking around the Gaslamp district in the evening.

SD Zoo, Balboa Park, Cabrillo National Monument, Hotel Del Coronado, La Jolla along the coast by the LJ Cove, Torrey Pines State Reserve, Self Realization Temple in Encinitas, Little Italy & Gaslamp Area and Whale watching.
Where to stay that is reasonable in SD..hope you are going before or after Valentine's day..I would check out
La Jolla they might have some great deals with ocean views for around $150 a night or less. Downtown SD, I would check out Holiday Inn at the Bay.
Have a great time in San Diego!

hotellajolla.com
ljshoreshotel.com
sandiego.com
sandiego.org
gaslamp.org

The Zoo & Balboa Park AND any one of the multitude of wonderful Mexican restaurants.

TT has a pretty good list there not sure what your budget is but we stayed at the La Jolla Travelodge and there is a Holiday Inn Express across the street. Several places to eat within walking distance and just a block inland from Wind-n-Sea beach.