I would recommend the Chain Bridge, the Royal Palace and the adjoining riverside area. Then hit the pubs and restaurants and enjoy nice cheap food and drink!!!!
I remember the covered market being good fun, and there were hot spa baths which I never got time to visit. The view from the top of the hill (at the monument) is spectacular.
You should certainly go to one of the Turkish baths. quite an interesting experience. and cheap too. also it's worth taking a boat trip (the english commentary was a bit dodgy on the one I went on, but you get the gist.) which should take you to Margaret Island as part of the trip.