Where abouts are you staying?
I take it your going for shopping etc so visit Victoria Square. Its a new shopping centre which feels like an outdoor shopping centre which is inside but take the cheque book as its quite expensive.
As said above, visit the waterfront area and also the odyssey arena is just across the road and over the bridge and you can look over the docks etc or visit the cinema and there are also a few restaurants in it, one of which is the red panda which was mentioned above but dont expect to sit for to long in there as the service is very quick but they always seem to want to pus you out.
In Belfast city centre, opposite WH Smith which is on Royal Ave near the city hall (the main street) you will see the tourist info place, pick up a What about guide book which is free and will list you all the events happening and also loads of restaurants and things to do and maps in it. I live a few miles from belfast and i usually try to get my hands on one as it keeps me up to date with whats happening!