There's a Tesco metro in the city centre, and also one down one of the side streets near the college- I can't remember the name of the road but it goes off Ipswich road as you walk up from the city. I'll try to find the name of the street for you.
I don't know much about the pubs (I don't drink) but I hear the Murderer's on Timber Hill is very good (my sister goes there sometimes).
EDIT: Yeah, there's a Tesco Express near college. As you walk up towards college from St Stephen's street, you come to a side road on the left called Grove Road. If you go down to the end of that street, the Tesco Express is across the road and to the left. Can't miss it.
There's also a big sainsbury's near the bus station.