Budapest Transit card

Mostly in the center, you can get around on public transport. There are 4 subway lines, trams, and buses. We used the subway on Adreassay Utca to go 4-5 blocks. You can cross the river on M4 or some of the trams.

But note that in Budapest, they check for your pass. So, I'd get the pass, and then you don't need to buy single ride tix.

Yes, a transit card is a good buy. I was in Budapest last summer for the F1 race weekend. I found a transit card very useful for getting around Budapest. Some of the prominent sights are long walks apart and all of them are uphill on the Buda side. Trollys for shorter trips and metro for longer are excellent.

Also, I only buy tranist cards, not "city" cards that include discounts to museums, etc. along with the tranist card.

My bath visit was to Széchenyi. Higly enjoyable, but very busy. We had to wait over an hour to get in. If I get to Budapest again I will try one of the smaller baths.

There is the Budapest TravelCard which provides for transportation only and there is the Budapest Card which includes a lot of tourist benefits. I havent met anyone yet that got their money's worth out of the Budapest Card, but never hurts to do the research based on what interests you. And finally, there are individual tickets.

https://bkk.hu/en/tickets-and-passes/prices/single-tickets-valid-for-one-ride/ (see the list on the right)

You can purchase the Cards, TravelCards and Tickets in vending machines and metro offices and BKK ticket offices; or you can use the BudapestGO App and use your phone as the ticket. I like paper so still do the paper.

There are no installed machines to check anything, except to validate individual tickets, before entering the transportation. Checks are random, sometimes at the entrance, sometimes at the exit, sometimes on the tram or bus by a plain clothes individual (who will put on an armband as identification).

If you are caught, the fine is expensive. So dont cheat.

If you are asking if the public transportation will get you to the sights, then you need to do some homework and learn the routes of Tram Lines, 2, 4/6, 19/41, 47/49 the route of Bus 16 and the route of the M1 Metro Line. Done correctly and depending on where you are staying these will get you within a 5 minute walk of 90% of the sights of Budapest. Sounds like a lot, but really isnt and the way the interconnect makes getting around very easy. Think about the trams as Budapest's cheap and better version of a HOHO bus.

You might also want to learn a few place names:
utca, abreviated as u. = street
út = boulevard
udvar = courtyard
tér = square

There is a hotel that use to advertise that they are on the famous Vaci ut. Well, the famous road is Vaci utca or Vaci u. so it doesnt hurt to know the difference. Andrassy is a ut, not a utca or a u. The M2 and M4 cross the river. Odds are you wont need either. The 47/49 and 4/6 Trams also cross the river and are more likely that you might use.

For bath house the easy choice is https://www.szechenyibath.hu/