Budapest, the bridges, the Parliament and Castle Hill are all very, very special when seen from the river; particularly at night when all lit up. Unfortunately the river taxi to Szentendre stops running in September. You could do an evening cruise on one of the tourist boats. Some have dinner, others not. I've done it a couple of times while entertaining friends and to be honest, as touristy as it was, I enjoyed it. There is better food than the boat food, but you know, for what it is it wasn't half bad.
FINALLY, someone spending enough time in Budapest. When do you arrive / depart?
With 5 days a trip to Szentendre (or Vac) is worth the effort. The trip to Szentendre is maybe a tad less intimidating as the departing station is very simple to navigate.
You often hear about Buda and Pest becoming Budapest. There is a third town that joined the other two in the union that generally gets overlooked: Óbuda. It's a pretty fascinating portion of town replete with Roman Ruins. Óbuda also has a market that you might do some research on. You might find that the Óbuda market is more Hungarian and less Tourist. http://budapestchristmas.com/advent-fair-in-obuda-budapest. It high on our list for this Christmas.