I lived in Belfast for over 6 years and I think it is a fantastic place for a weekend. The city hall and the Ulster Museum are well worth visiting.
If you want to get a different perspective, you can get a 'Black Cab' tour which brings you around areas of the city affected by the troubles.
For a night out, the south side around Queen's University is the best; several clubs and pubs, you will be spoilt for choice and the beer is cheaper than in the south but need to be careful of not going out in the wrong area as a strong Southern Irish accent may cause you a bit of aggro. Avoid the west area i.e. west of the Westlink by-pass and any where you see red/white/blue paving stones and you will be fine.