I can't answer your food question specifically.
Generally, there are quite a lot of different places to eat in 'Grand Central' (the area above New Street Station) or across in Brindley Place (by the canal Network.
In terms of what to see, have you been before?
What interests you ?
If you are coming Thurs - Sun then I would recommend Birmingham Museum and Art Gallery. A lot to see there, and the building itself is rather nice. They also have nice Edwardian Tea rooms.
From there, wander across and go into the Library. Architecturally controversial (I like it, but lots like to moan). There is a roof garden / viewing area you can go to and look out over the City. Also a lovely Shakespearian Library to visit.
You can wander through the ICC (where the Symphony Hall is) and you come to where the canals are and that's nice to walk along for a little bit. You can go on a boat trip if you like, or walk toward Broad Street to see Ozzy's bench.
The Bull Ring has St Martin's Church which is lovely, nestled in amongst a lot of redevelopment and shopping. There is a Bronze Bull people tend to have their photograph with, and (if that's your thing) you can find Paddington sitting on a bench in Selfridges.
The big mechanical bull that was part of the Commonwealth Games opening Ceremony now lives in New Street Station.