Among visitors to Budapest we distinguish 2 groups, short term and long term travelers. Short term visitors come for holiday or business. Long term visitors come to live here for months or even years.
Short term travelers usually spend 2-3 days on average in Budapest. Choosing the right accommodation depends on your budget, the partner you travel with, and the purpose of your visit.
Budapest is a relatively cheap destination compared to most of the western countries. Either you can choose a higher standard place for the same amount as at home, or book an even cheaper one than the cheapest in your hometown.
Depending on who you travel with, you will need different accommodation types. You can travel alone, with your partner, friends or family. If you travel alone, you choose your place to stay according to your standards. If you travel with your loved one, you probably will not stay in a hostel with a bunch of other dudes. If you travel with your friends, you can stay in a cheap hostel or you can rent a whole apartment. If you travel with your family, I am sure you would like to stay in a calmer family friendly half board place.
Your purpose of visit can define the place where you want to spend your nights. If you are on a business trip than you will choose a hotel where there is a good Wi-Fi connection, a meeting room, and everything that a business person needs to be successful. If you visit the city of spas, you will need a hotel which offers wellness, health, and medical services, or located near one of the most famous baths, such as Széchenyi Spa and Gellért Spa. If you are party animals, you will certainly stay in the party district close to the clubs and bars.
Budapest is a metropolis and it has a lot of different areas where you can stay. If you want to feel the city vibe, then downtown area is yours, if you like the panorama you had better book a room by River Danube where you can be amazed by the House of Parliament, the famous Chain Bridge, or the Castle of Buda. The city has more peaceful places like the City Park, Margaret Island, or the hills on the Buda side.
If your trip is not organized by a travel agency, you can use the most common accommodation websites such as booking.com, agoda.com, airbnb.com, or even couchsurfing.com (which offers free places to stay at locals) when planning a trip to Budapest. You can also contact the hotels directly as they offer special discounts on their websites.
If you are planning to stay longer in Budapest, you can rent a flat or a house, for around 400-500 euros per month on average. Remember that landlords usually ask for a 2-month deposit.