Taxi from train to apartment

The currency in Hungary is called the Forint. They don't use Euros.
There is a Uber-like service called Bolt in Budapest. Maybe that would be a better choice.

The last time I was there, there was an ATM in the train station. That was a few years ago, but I don't know why they'd remove. it.

Until James E. chimes in, he recommends:
Transportation: City Taxi https://www.citytaxi.hu/

They use Euro and Forint almost interchangeable. Often will give the price in Euro first. All meaus had both Euro and Forint listed. At that time the Euro price was cheaper. Just check with the driver. The exchange rate was fair. Double check if credit card is acceptable. AND -- watch for a choice on the screen for how to charge your card - dollars or Forint. For us it was always option two for charge in Forinet. Our limited experience with the metro is that it did not take credit cards.

I arrived at Keleti last fall. As you face the front of the station from the inside, left of the doors is an OTP bank ATM.

Turning around after you've used the ATM, looking back into the station and just a bit to your left, there is a large central staircase down to the metro. On that lower level are ticket machines (look for the purple stripes around the top of the kiosk) which did take my US credit card.

EDIT: In Google Maps I'm only finding a Euronet ATM, but the one I used was definitely not that. The bank ATM was next to the Euronet one.

I had no problem using my credit card in the Metro. That was in January.

I'd take the taxi, and yes city taxi. Call when you get off the train. Facing the front the taxinline is out the doors on the right. They take Forints, Euro and credit cards. Euro is fine for arrival but get some forints from an ATM before very long as, while all the tourist places take Euros they do it at a profit for themselves. Cant blame them, as they have to change the prices and menus with the exchange rate changes and then they have to go change the money to forints.

As you get away from the tourist hotspots and into the best parts of Budapest, euro will be harder to spend.

Karen, we used the recommended city taxi (August) upon arrival in Budapest. We had planned to use a credit card, but their system was down. As previously mentioned they accepted Forints or Euros. We had both on hand. Great customer service. Well organized company. Easy peasy and affordable. Hugs to Barley!!

I've got a handful of great stories about City Taxi; wonderful company.

I did a search yesterday trying to find a last minute taxi for our daughter in Budapest to get from her hotel to the airport. We followed James' suggestion for City Taxi and it was perfect! Thanks for the great recommendation!

Glad it worked out. These guys have been great over the years. One morning I called for a taxi to the airport and they said it was a busy morning and it would be 20 minutes. I didn't have 20 minutes. The dispatcher said sit tight and one would be on the way. He called another company to pick me up. On another occasion the dispatcher spent at last five minutes on the phone with me trying to figure out where I was so they could send a car. I just couldn't pronounce the street name. But he didn't give up, asking for descriptions of what was around me. On a third occasion we were in an accident. Before the driver got out of the car he called a car to come get me. I paid the first one and got in the second one. When I tried to pay him he told me to fare on the meter was too high because it included the start fee and it wasn't fair to charge me the start fee twice. All the companies are heavily regulated so I suspect they are all pretty good, but City Taxi gets my business.