Budapest has a very efficient public transportation system called BKK. There are various means of transport (bus, metro, tram, trolleybus, suburban railway), which generally run daily during the hours 4:30 AM – 11:30 PM. There are also buses that run outside these hours. You may find the online route planner and the BKK Futar mobile App useful.
A monthly pass, valid on all means of transportation and for all transfers within the city and its suburbs, costs about 10,000 HUF. The pass is valid for 30 days, and the first day of the 30 day period can be any day of the month. Single tickets and booklets of 10 tickets may also be purchased.
Note: As you are not a Hungarian student, you must obtain the full-price pass, not the student one. Having the wrong pass may result in a fine of 16,000 HUF or more.
Taxis in Budapest have uniform fares. A trip within downtown costs around 1,000–3,000 HUF, and taxi companies have online fare calculators. Make sure the taximeter displays the actual fare during the ride.
For more details and a list of taxi companies, see:
Use extra caution when riding a bike in Budapest, as rules of the road and driving habits are quite different in Hungary than in North America. Even if you ride in a bike lane, be aware that drivers do not always give the right of way to bikers.
Budapest has a public bike-sharing system called MOL Bubi. It has many docking stations all around the city, so you can just grab a bike and go. To get a pass, use your residence card. About prices and how to get a pass or ticket, please visit the following site: http://welovebudapest.com/budapest.and.hungary/grab.and.go.ride.the.new.mol.bubi.bikes.all.around.budapest
Boats are a nice way to do sightseeing in Budapest. There are various companies offering boat trips for tourists. It is also worth checking out the BKK (public transport) boat. Check the schedule of boat services D11, D12 and D13 at http://www.bkk.hu/en/timetables/.
Note: The monthly public transport pass is not valid on the BKK boat, and a single ticket costs 750 HUF.