My favorite city in Andalucía, without a doubt, is Granada. There is nothing like it.
How old are your daughters? It doesn't matter all that much...they'll be very safe...as long as they are "somewhat" street smart. All in all, however, the city is very safe.
Two years ago I stayed at a wonderful Hotel...the Aben Humeya (
www.eel.es/granada/hotels/aben/aben.htm). It's in a very good location. The rooms were huge. They also had an extremely reasonable and good restaurant within it.
As to the price...I'm not too sure. When I went they had just converted to the Euro system and I had already prepaid for the stay (I was there for an international conference) with a reduced rate.
All of us who stayed at the hotel were extremely content...more so than those who stayed up the street at the more expensive one.
Give it look and see.
Hope this helps,
Sheryl