There's always the Titanic Quarter if that interests you? I cant really think of anything else that distinguishes Belfast from any other city apart from that to be honest...
Food wise there are plenty of your chain style restaurants in Victoria Square which are close and should fall within your budget e.g Wagamama, Nandos, TGI, Spur Steakhouse, Chiquitos, China King Buffet etc. If you are still around at lunchtime tomorrow get yourself over to Boojum for an awesome burrito, there is one on Botanic Avenue and one on Chichister Street (closer to you, around the side of Victoria Square shopping centre) there will be a queue out the door but it moves very quickly, will cost you about £6 including a drink, in exchange for a burrito the size of a small baby.
Scalini (Botanic Ave) and Villa Italia (University Rd) are decent Italian restaurants, should be able to get a couple of courses for within your budget. Again struggling to think here, but if I get any ideas i'll come back.
Edit - Oh yes Tao Noodle Bar (Shaftsbury Square) is great for not your average chinese cuisine, they also have a menu specifically for the local chinese population which you can ask for with some more "true to home" meals on there. Its will easily feed you for £25, it looks more like a small cafe than a restaurant and is not usually busy in the evenings but dont let that put you off, its great.