[Budapest] Take a city tour or get a bike and ride around yourself?

I'm not at all a fan of hop-on/hop-off buses. Too often they seem to involve a lot of standing around at the bus stops, waiting for the next bus. I'd rather take walking tours or just wander around by myself on foot. James E has mentioned a tram in Budapest that runs along the river for at least part of its route. That would be scenic. It may be Tram 2.

Budapest is a pretty city; it does have a lot to enjoy even if you never go inside a building. However, that doesn't mean there aren't wonderful museums and buildings to tour. It's a matter of your personal preferences and your pocketbook/wallet. The Parliament Building entry fee is very, very high unless you have an EU passport. Other options are mostly a lot less expensive. If you haven't seen something similar elsewhere in central/eastern Europe, I recommend a visit to the House of Terror. Buying the ticket a few days ahead of time might be advisable. I don't know whether there are capacity controls in place, and I got hung up in a 20-minute ticket-buying line on my 2018 visit.

I'm a Cold War junkie and thought Memento Park was a lot of fun. It's about 7 miles from Parliament, so the distance is reasonable for a bike ride. I don't remember the terrain, though; I took a regular city bus. There's also a dedicated bus to the park, but I think it runs less frequently. It may also be more expensive.

Budapest is the rare large city where I decided the city sightseeing card would pay off for me. One reason it paid off was that I took the two included Cityrama walking tours, one on each side of the river. I enjoyed them.

I have no experience riding a bike in a European city and cannot make a recommendation on that one way or the other from a safety standpoint. Buda is very hilly, though.

A day-pass for the city transportation is comparatively cheap, and you will certainly want some form of transportation to supplement walking. Be aware that ticket inspectors in Budapest are very active. If you don't have a day-pass, be sure to hold on to your single-ride ticket and be prepared to show it.

I believe the Parliment ticket is only 10 USD though

https://www.parlament.hu/web/visitors/ticket-prices
3200 HUF which should convert to 10 USD. Pretty cheap for most museums/buildings

The two times I went to Budapest, I used Rick Steves’ latest guidebook: https://store.ricksteves.com/shop/p/budapest-guidebook and took his self-guided walking tours and loved it. You’ll be there when Andrassy Ut plain trees shade the street. If you can take a taxi one night and ask the driver to drive past the illuminated sites do it. I would spend one morning at the Széchenyi Baths when the elderly men stand along the edge of the pool and play chess.

There are several Euro cities I would never ride a bike in....and Budapest is on that list. Observing as a pedestrian, it is my opinion that it is not bike friendly (at all).
Every stop on your itinerary is certainly worthwhile - but get there some other way. Public transportation in Budapest is very good, lots of variety, and inexpensive.

I agree, Budapest doesn't seem like a bike-friendly city, and it has very good public transportation (including a tram system whose tracks in the streets can be very bike-unfriendly). Pest is flat enough but Buda is on a steep hill. I didn't go to Memento Park. Besides, riding a bike means paying lots of attention to steering and traffic instead of enjoying your surroundings.

If you can find the RS Hungary or Budapest guide in your library, check it out and maybe photocopy some pages to take with you. (Or buy the whole thing, in fairness to our host, but I wouldn't for a two-day stay.) There are suggested walks and good info about the sights and how to get around.

I agree with acraven about the House of Terror, where I spent almost a whole afternoon. The art museum next to Heroes Square, the Great Synagogue, the Great Market Hall, the Opera House, and St. Istvan's Basilica all appealed to me as well as the sights you mentioned. (I missed Parliament.)

James E is our leading authority on all things Budapest and anything he suggests will likely work well for you, but he may be traveling now.

Hey, you're right: That must be a reopening special at the Parliament Building. It looks like it's valid only until mid-September, so definitely take advantage of the opportunity if you can. The going rate was the equivalent of about $25 in 2018.

I see, so it has to be with public transportation then. Would you recommend a tour bus/group then? Or just local buses when going place to place.

I'd say trams on the surface and the underground for longer distances. For instance, our hotel was near the Great Market and I got on the underground at Kalvin Square, changed lines, and got off at Heroes Square. Too far to walk but an easy ride (and the Andrassy underground line is one of the oldest in Europe, an experience in itself). Of course I missed the streets and sights in between, but I saw a lot of those by foot and/or tram. I had some kind of multi-day pass that made it all very easy.

Look at a guidebook.

If you have time to read and like to read, I would highly recommend Twelve Days: The Story of the 1956 Hungarian Revolution by Victor Sebestyen. It is well-written and gives much insight into Cold War Budapest and its desire for freedom, especially among students. There are some good photographs in it. I was walking along a street in Budapest with friends I was visiting there, looked to my left, saw a movie theater, and said, "Hey, that theater is the theater that students holed up in in 1956!" I dragged my friends over to it, and we circled the building, finding some plaques and a monument out front that confirmed my thoughts. And it was still showing first-run films. History is around every corner in Budapest.

Especially because of the hotel you are staying at, you will need a metro pass to get into the center (https://bkk.hu/en/tickets-and-passes/prices/travelcards-valid-for-one-or-more-days/); get the 72 Hour Budapest Travel Card (you can buy them from a vending machine at the Corvin-negyed metro station near your hotel.

With only two days I would stick to the outdoors via Metro Line and Tram.

One day you could take the M3 metro one stop to Kalvin ter and change to the 47/49 Tram which will take your from the Gellert Hotel to the Great Market Hall (Visit) to the Great Synagogue (short tour and a walk i the lower part of the Jewish Ghetto area) to Andrassy ut. (walk to Hero's square and take the M1 Metro back to the start)

One day you could hop on the M3 again, and take it to Deák Ferenc tér and then a short pretty walk through great architecture to the river front. At the river front you can get on the 2 Tram wich will take you from the Great Market Hall (been there, done that, so get on heading to your right) to the Parliament Building (view the outside, see the old public buildings and banks in the area, play in the fountain).

Walk north up Falk Miska u. (antique shops) till you find the 4/6 Tram. Get on going to the left. It will cross the Margit Island Bridge and make a stop on the Buda side. Here you will find the 17/19/41/56 Tram. That will take you to the Chain Bridge and the Funicular up to the Buda Castle Hill (go visit)

Walk back down the hill and get back on the tram and get off at the Gellert Hotel Stop (great bath house and great history). Here you will also find the 47/49 Tram that will get you home.

Okay, my two cents on how to spend a two day tour.

If you want to raise the ol’ heart rate, walk up the hill to Buda Castle instead of taking the funicular. A friend and I were definitely going against the flow when we did that, but there were a handful of others who joined us in this endeavor.

James has a great plan if you want to follow it. And I would also recommend the Sebestyn book that Dave mentioned.

Thank you for the feedback! We ended up planning the 1st day to be the Széchenyi Thermal Bath (~3-4hrs), followed by the Parliment building and a Cruise/dinner at night. Day 2 will be as James suggested, taking a tram to the Market, Heros square, and still split between the Synogogue or Buda hill (but one or the other), the Gellet bath, finished up with a pub crawl at ruin bars.