Central Square Hostel
address: pl. Rynok 5
phone no.: +380972224136 +380322546169 +48123765151
prices: from 65 UAH (8 USD) [2010] off season and from 95 UAH (12 USD) [2010] in season
website: http://cshostel.com/ Facebook

Retro Hostel Shevchenko
address: prosp. Shevchenka 16
phone no.: +380322403761
prices: from 40 UAH (5 USD) [2010]
website: http://www.hostels.com/hostels/lviv/retro-hostel-shevchenko/20197

"Elektron" Hotel
address: 4 Kvitky-Osnovyanenka Str. (last floor)
phone no.: +380322335227
prices: from 20 UAH (4 USD) [2007] per person in a room for approx. 8-10 people
hot water: 6 - 9 a.m., 6 - 9 p.m.
in general: probably the cheapest hotel, 30 minutes walk from the city center, pretty much ugly, don't turn back sober :)

"Lviv" Hotel
address: prosp. Chornovola 7
phone no.: +380322423555 and +380322423270
website: it exists, but it's completely out-of-date
rooms: mainly single and double/twin, some for three or four people
prices: from 55 UAH (11 USD) [2007] per person
hot water: supposedly non-stop
in general: ugly on average, close to the city center, acceptable, but you should have a sleeping bag ;)

Where to stay overnight in Ukraine

Private apartments
I provide the information only personally.