I can speak on this subject.
Last year me and the wife went out on an assignment for 23 days. The clients guest were staying at the Boscolo (5 star), but when we were walking abound, the 4 seasons Gresham Palace (overlooks the Danube and by all accounts is very swanky. We stayed at the Novotel on the Buda side. Its right next to the tube station so ok for getting about. not too pricey and more of a business hotel.
Places to go on the weekend are the ruin bars (evening time for a drink), day time, fisherman's Bastion, The Citadel (big fort on top of a hill that overlooks the Danube),
What ever you do, take and evening river cruise ( don't go on the small craft that looks like they will sink) go on a panoramic boat.
I cannot recommend enough the Quayside restaurant (boat restaurant - Static) called the the spoons. Insist you you have a table on the riverside as when evening comes the view is so romantic.
Finally, if you get time but not a serious necessity, the Szechenye Thermal Baths are hot springs, but quite expensive.
Don't bother with Memento Park (its were they parked all of the old communist statues) truly not worth it.
If you go visit the parliament building, you must take time to walk down to the river side and turn left to walk towards the cast iron shoes on the riverside which is a memorial concept in remembrance of the victims of the pro nazi Hungarians who regularly cause Jews to disrobe and then were executed with their bodies allowed to float down river for all to see. Its a very moving tribute.
Beyond that it you still have time, there are flea markets and shops that women are drawn to.
Finally, go over the chain bridge and ride the funicular up to the royal palace.
We loved it. good food and live entertainment at http://www.ladocafe.hu . this was great food and drink and 150m from the Novotel, alternatively you could use McDonalds which is also 150m from the Novotel LOL
Dario