I just returned from Prague on a two-night layover because it was on the way somewhere else and it saved a lot of money over flying to Vienna. Train from Prague to Vienna was $30 USD.

I'm an older single woman, and the city is absolutely safe. I'd read a lot about pickpockets but didn't notice any problems. A local I rented from told me to not take cabs from the airport. There is a scruffy bit around the train station, but that's typical.

Transportation is easy. If you go to the castle, and you should, take the 22 tram, not the metro to Hradcanska like I did. That station is a long way (uphill) to the castle, and you can't see the castle from there if you come our the wrong side of the station, you have to find the signs and follow them. Anyway the 22 tram goes right to the gate.

I rented a studio in Vinohrady for 35 Euro a night.

At the time I came, months after reserving, repairs were being done to the building, so I was put up in different rental at the same price: 2 br, lr, kitchen, elevator, on Bilkova street two blocks from Old Town Square. This apt usually goes for 55 euro.

Not elegant, but adequate, well located, and Ivan Falta is a really nice guy who's lived in Prague all his life and speaks excellent English. For true budget I would use his firm again.
http://www.accommodation-prague.cz/sl/sl_en.html

The Castle Steps, featured on 5 takes Europe is more expensive, but includes breakfast and seems might be worth checking.

http://www.castlesteps.com/index.htm