Yes, the 24-105mm f/4L is excellent on a crop body. It's a 'relatively' inexpensive L lens, which is good, because with the shorter L's (e.g. the 16-35mm f/2.8L) a lot of what you're paying is better IQ at the edges of the full frame, and those don't matter with a crop body. The main problem with the 24-105mm on a crop body is that the wide end isn't wide, but as long as you're willing to change lenses you'd have that covered with the 10-22mm. For me, I could not leave the 24-105mm on my camera most of the time, as I frequently grab my camera to take pics of my young daughter in the house, and I need wider that 24mm for some of that. So, for me, the 17-55mm f/2.8 is the ideal 'leave on the camera' lens (a bit more reach would be nice, but I'm not willing to trade f/2.8 or the wide end for that).


As a side note, when asking for lens advice it often helps to list the other lenses you have, either in your post or in your Bio.