A guy from my hostel is wondering how much to expect to pay for a taxi to the Szechenyi Baths and back to the airport since he has a six hour layover there.
As bonus questions can he pay in Euros or will only Forint be accepted, and is there any way to get a return fare?
He expects that public transport or airport shuttle will eat into his time too much so it has to be a taxi.
The "official" taxi company of Budapest Airport is Főtaxi.
From the airport to the Szechenyi Bath the price is 21-22 EUR:
Back to the airport costs 16 EUR:
You'll get a discount card at your first travel, you have to show it the second time to get the discount rate.
I've never payed Euros but I think they accept it ( they printed the price also in Euros ). According to the airport's homepage you can also pay with credit card:
All cars are equipped with POS terminal, therefore passengers can pay with credit card as well.
Tripadvisor has an extensive description on how to get from the airport to anywhere in Budapest. Your friend might be specifically interested in option 4:
Taxi Option 4: Arrange with a Specific Airport Transfer Service to meet you inside, as you exit the secure area, with a sign with your name on it
They list three companies. I have tried two of those companies and I don't regret it. The driver was on time. From the airport to the city we paid 22 euro and on our return trip we paid 18 euro. Both times we paid with credit cards on the onboard terminal.
