Taxi rate in Budapest

https://www.taxi-calculator.com/taxi-fare-budapest/385

I wasn’t able to use the link in the post above (it would never give me an amount).

However I used the City Taxi app calculator and it says @ 2,500 ft. (@ $7). Of course, I picked a hotel in that area at random since you didn’t specify. If you are closer to Podmaniczky u, you could take the 70 or 72M bus easily. And if you are closer to Andrassy ut, you could take the M1 line very easily.

If you think you will use taxis much (or even just once or twice), set up the City Taxi app at home before you leave.

Here’s a really great post on getting around Budapest. https://community.ricksteves.com/travel-forum/hungary/transportation-in-budapest

Of course, the M1 metro is less than a 5 minute walk from your hotel, and M1 will cost you about $1 to reach the bath house. Less if you bought a TravelCard.

As others have shared, you're better off taking public transportation which is safe, clean, and easy. Széchenyi has a stop on the M1 line. Your chose neighborhood is also quite close, so you'll not only save time but money in choosing to use public transportation.
If you provide your hotel name, several people here can give you precise directions.

If you prefer taxi service, City Taxi can provide you a quote.

Taxi rates have gone up in the last year. What was a $25 ride from the airport to my accommodations is now $30.