There are several spots in Recoleta where you can stay for under US$100 - The Juncal Palace, The Art Hotel, Recoleta ApartHotel - the first two have websites that are easy to use (juncalpalacehotel.com.ar and arthotel.com.ar), the latter you can book through hotels.com.

Juncal Palace is pretty much a place where you just have a bed to sleep - it's very inexpensive, is clean and well kept, but you have to step outside your room to change your mind... still, if you're not spending much time in your room, it's a great cheap option. Art Hotel is a bit nicer, with somewhat bigger rooms, and some extra services, like internet in the lobby, and a staff that speak English. Recoleta ApartHotel is another step up, and I've had friends stay there and love it, though the one comment was the lack of staff who speak anything other than Spanish.