Prague is awash with backpackers and hostels IF you come in summer and can find them. Hostel Elf was my choice, 250 czeck krones, 6$, including breakfast(very small) sleeping in a dormitory, common but very good bathrooms, hoooot showers, very nice people. More and other rooms on offer. And once you check out the metro system it is very easy to get there.

Being approached at the train station by a group of men was a bit unsettling. A woman travelling in Eastern Europe, I was a bit reluctant to take the offer of a "room to stay". However, I took the leap of faith and ended up housing for US$9 a night in a nice apartment with a wonderful old lady. I later found out that this is a common custom. So, go ahead, take advantage of the wonderful hospitality and save yourself time and money!

The Boathouse is a hostel about 20 minutes out of central Prague right on the river - it is cheap, fun, they cook great meals, very social, and the ride on the tram into the city is a very local experience! Even though it's further out of town, there are trams going very frequently and it is an enjoyable and pictoresque ride along the Vltava River. I would just stay here for the social environment, if not for the convenience of meals and the friendliness of the staff! You can also use the row boats on the river right outside the hostel!