Budapest is definitely one of the hot cities among cultural tourists these days, and for good reason. It’s unique and historic while remaining quite cheap by most standards. Unlike Prague, this city hasn’t yet been able to adjust its prices to meet (and frustrate) the new interest.
Hotels in Budapest are particular bargains, with decent standard double rooms at mid-priced places going for what you’d pay for a hostel bed in London. Rooms in the cheapest Budapest hotels might not be up to the standards you are used to, so it could be wise to pay a bit more for a better place. Hostels in Budapest are also great bargains.
Many of the most popular attractions in the city are free or very cheap so those on a backpacker budget will be able to experience everything they’ve come for without going broke.
Food and drinks are also quite cheap by European standards, especially the local food (which can be quite heavy) and items from street stands or fast food places.