A Range of Prices
Hostels and hotels in Hungary can vary dramatically in cost. In rural areas you're likely to save some money, but there is a more limited selection, so you may not find the super cheap options that you can find in Budapest. In Budapest in particular, there is no shortage of hostels for those on a budget. You can find them throughout the city, but look for a place that is centrally located, or easily accessible by public transportation so that you can make your way around the city to all the attractions and activities with ease.
There are some very nice mid-range and high end hotels as well. You'll find a wide variety of the American chain hotels, so if you're looking for a particular hotel, there's a good chance you will find it. Alternatively, your money will go a lot farther if you choose to stay at a locally owned facility. The facilities are usually of a high standard and the cost is a fraction of what you would pay for a chain hotel.
Location and Timing
Dorm rooms are generally the cheapest way to go in Hungary, but you can usually find some good deals on double rooms in budget accommodation. If you stay a little out of town, you may save some money, but make sure you are near public transportation that is reasonably priced. Otherwise you're likely to pay more in time, effort, and money than you saved on your accommodation.
Like elsewhere, traveling in the off season is a good way to save money. Make your reservations well in advanced and you'll likely get a better deal as well. Also, travel with a larger group and you can rent an entire dorm room of the appropriate size. This will ensure that you don't have to share the room with strangers, but you still get the benefits of staying in a dorm in a hostel. Most hostels do provide a decent sized breakfast and a kitchen for cooking. The kitchen can help save you a good amount of money in food costs as well.
Hungary has a wide range of accommodation types. You can find countless hostels, hotels and luxury accommodations throughout the country. There are also many camping opportunities, particularly in the most rural areas.
Village tourism is on the rise in Hungary as well. Outside of the cities, this is a great way to experience real life in Hungary. You can learn more about these opportunities through the Federation of Rural and Agrotourism and Centre of Rural Tourism. Alternatively, you may be able to find independently managed rural houses available for rent. One such example, the Wild Grape Guesthouse, is close enough to Budapest that you can travel into the city, but also near at least one national park. This is a fun alternative to staying in the city.
Budapest has, easily, the highest selection of sleeping options in Hungary. There is no shortage of hostels around the city, but most are located in the Pest side of the city across from Castle Hill. They are close to plenty of restaurants and entertainment options and are often near the city's downtown area. Many provide breakfast in the price of the room. Many of the more expensive and nicer hotels are located across the river in Castle Hill. The air quality is better in this area, and you are near some of the nicest attractions, but it is also more removed from the downtown parts of the city. Many of the nearby restaurants are more expensive and cater specifically to tourists, so they loose a little of their local charm.
Another fun option in Budapest is to rent an apartment. They are spread throughout the city so make sure you choose one in a convenient location or at least near public transportation. If you're arriving in the city by train then you will likely be greeted by some older women that have rooms available in their house. These can be a great deal, but make sure you confirm the location before you hop in a car with a stranger. You might end up well outside of town.
Siofok is a small town located on the south shore of Lake Balaton. It's a charming little town that is a popular resort with international travelers as well as local Hungarians. There are a small handful of good places to stay. If you're traveling during the peak season it is recommended that you make reservations well in advance. The popular places do tend to fill up and you'll likely get the best rates well in advance. You'll want to stay near town, but also close to the beach so that everything is easily accessible. Many of the hotels are very reasonably priced and if you're coming from Western Europe then you will be pleasantly surprised with the value. Mid-range hotels usually offer the best value as they are only a few dollars more than the budget options but the condition and quality is generally substantially better. The locations are usually good as well.
If you're in town during the low season then you can get some particularly good rates. Some places may not be open, but those that are will offer you a steal. The crowds will be less as well, but the weather won't be nearly as pleasant.