Trains are really easy to catch
Bikes can be rented from various companies all over the city which makes getting around really easy
Baths - go and check out the baths in Budapest, some days only men are allowed at certain baths so double check before heading there.
Great to do the night swimming on a Friday night to look over the city.
Szentendre - Day Trip
Take a train around 1 hour of of the city to explore an old town of Hungary. Great art and culture within the town.