When I want a walk-around zoom on either my crop or FF cameras I use 24-70 or 28-135. (I don't have the 24-105... the 28-135 is a "poor man's substitute" for it, IMO).
I don't know why you don't just use the 24-105 that you already have.
I have no plans to buy additional "crop only" lens that can only be used on my 7Ds. I want lenses I can use on both, as much as possible. The only "crop only" I have is an ultrawide: Tokina 12-24/4 (which, it so happens works, on FF as wide as 18 or 19mm).
But if you really want something specific, just for 7D, some good choices might be:
EF-S 17-55/2.8 IS USM
EF-S 15-85 IS USM
Sigma 17-50/2.8 OS HSM
EF-S 18-135 IS (not USM, often a "step up" kit lens for 60D, 7D)
Tamron 17-50/2.8 non-VC (slower focus)
EF 28-135 IS USM (buy it used, many have been sold as kit for 40D, 50D, 7D.... it's a good lens and can be bought cheap used, as low as $200 US... it's just not very wide on a cropper)
EF-S 18-55 IS (non-USM, cheapest, "kit" lens)
Or, how about a prime or a macro/prime? Personally I'd like to try the 40/2.8 "pancake" and the Tamron 60/2.0 macro/portrait. Sigma 30/1.4 or Canon 28/1.8 are nice "standard" primes. Some are "crop only"... others aren't