There is not a single Hostel in all of Santa Fe, but some of the Hotels will rival in price any backpackers hangout elsewhere. Santa Fe has an abundance of Hotels to choose from and nicer two to five star places can be found with a quick stroll around the San Martin neighborhood. Following is a list of the cheaper places, don't expect anything glamorous and you will probably witness and unsavory transaction or two at some point.
The cheapest joint in town is the Hotel Rivadavia (Single: $7, Double: $14, Triple: $21, Rivadavia 2847, Tel. # 03424533143) and it is definitely sketchy. Located in the back of a long hallway it seems to be hiding from the scrutiny of scrupulous society. A smoke filled lobby and "working girls" are common, but the rooms are secure, have private bathrooms and television. Just don't think of what is going on outside of your private sanctuary and you will be just fine.
Hotel Apolo (Single w/ telivision and bath: $15, Double: $23 ect., Single w/o tel. and bath: $8, Belgrano 2825, Tel. # 03424527984) is a clean and functional hostel located directly across from the bus station. The nice woman running the place has been doing so for 30 years. Private bathroom and television double the price of a single room.
Emperatriz Hotel (Single: $22, Double: $29, Triple: $39 Irogoyen Freyre 2440, Tel. # 03424530061) has a starless rating, but is a definite cut above the rest of the hotels mentioned as far as tranquility and calm atmosphere goes. Located in an old mansion it has high ceilings, a plaza like interior, nice clean rooms and helpful reception. All rooms have private bathrooms and television. Popular amongst the few travelers that Santa Fe receives.
Amanacay (Single: $11, Double: $16, Triple: $26, 25 de Mayo 2692, Tel. # 03424565052) has a great location right near the San Martín strip. It has affordable rates, clean rooms, private bathrooms, television and is completely stuffed full of mirrors. The amount of reflective material on the walls indicates that the hotel may be used occasionally for hedonistic purposes by the locals, but in general expect a quite atmosphere and a good bargain.