Budapest is a beautiful city, especially at night! The city is set around the Danube River with the "Buda" side and the "pest" side. The public transit system (bus and underground rail) are easily navigable, cheaply priced, and safe. Otherwise, taxis are an easy transportation mode too.
The Parliament tour is worthwhile and you get to see the Hungarian crown jewels. The best view of the city, again especially at night, is at Fisherman Bastion by Matthias Church. If you enjoy the opera, the Opera House is gorgeous and the shows are shown with English and German titles above the stage. If you enjoy history, the Museum on Terror and the Shoes along the Danube River are must sees then.
If time allows in your 2 days, I highly recommend a trip out to the Széchenyi Thermal Baths (there isn't much to eat around there so eat before hand or bring snacks). The baths are large and you can easily spend an enjoyable, relaxing afternoon there! Also be aware if going during a weekend because they have night parties with djs and lights, especially in the outdoor bath.
Enjoy the food & wine! My favorite is the mulled wine during colder weather. The oldest restaurant with excellent food and atmosphere is Szazeves Étterem- great for dinner.
Have a great trip!!