Can't believe you are going to the country that Conde Nast Traveler rated as tied for the best destination in Europe this year and you aren't spending more time. You have probably seen this. All but a very few seconds of it are filmed in Budapest http://www.ispot.tv/ad/7wvw/viking-river-cruises-see-things-differently- But we all have our schedules to keep, so:
The three hotels nearest that I know to be decent places are the
Sofitel http://www.sofitel.com/gb/hotel-3229-sofitel-budapest-chain-bridge/index.shtml which claims to have rooms starting at 127 euro,
Intercontinental http://www.intercontinental.com/hotels/gb/en/budapest/budhb/hoteldetail?qAdlt=1&qBrs=6c.hi.ex.rs.ic.cp.in.sb.cw.cv&qChld=0&qFRA=1&qGRM=0&qIta=99504425&qPSt=0&qRRSrt=rt&qRef=df&qRms=1&qRpn=1&qRpp=10&qSHp=1&qSmP=3&qSrt=sBR&qWch=0&srb_u=1&icdv=99504425&siclientid=1911&dp=true which is a nice larger box hotel,
Marriott http://www.marriott.com/hotels/travel/budhu-budapest-marriott-hotel/ another very nice box hotel with excellent ratings;
Last but closest, the Four Seasons which at one of the top rated hotels in Europe is not worth looking up the web page for.
There are some other smaller hotels further inland but these three will put you in eyeshot of the pier and they are all nice and reasonably priced.
TAXI RIDE: EDIT: Yup I mangled this. I-Pads and I don't get along too well. Corrected below:
When you get to Budapest, get your bag, look for the sign that says nothing to declare. Go through the nondescript black glass door and you will find yourself in the Arrivals Hall.
Continue walking straight (past all the private taxi drivers hawking their services) and in about 40 feet you will find the door to the arrivals curb in front of the airport.
To your left you will see the Fotaxi Kiosk. This is the contract taxi company for the airport.
Tell the person in the kiosk where you are going, he/she will give you a slip of paper and you move about 30 feet to the first cab in line where someone will help you with your bags and open the car door for you.
Give the driver the slip of paper and 30 minutes and $35 dollars (including a small tip) later more or less you will be at any of the hotels mentioned.
You pay the driver, not the kiosk person. You can pay with a Credit Card, or Euros or Hungarian Forints, or probably US Dollars (but check with the person in the kiosk on that one). The cheapest way will be the credit card or the Hungarian Forints. I have been a lot of places and few are this easy and this cheap.