Really depends what sort of food you want - try Borough Market itself, also places like Leather Lane Market, the indoor market near Greenwich is also good.

In terms of places to go and eat - agree with the others avoid the west end if you do want to eat there go to the back streets e.g. back of St Christophers Place.

Problem with recommendations is that it is so hard to get it right e.g. I don't like Bread St Kitchen as I think it is well overpriced.

For good steak try Santa Maria or Hawksmoor, other places we go to a fair amount are Yalla Yalla (for lunch as you can grab and go).

Also have a look for vouchers and offers plenty of those around at the moment to save some cash especially in Jan often really good 50% deals about.