I have the 7d also, and a 70-200mm F4 L IS, and it's the sharpest lens I own, especially on a crop sensor camera like the 7d.
I upgraded from a Tamron 70-200 (older model) and the difference was huge in all aspects.
The IQ was better, less CA, the IS is way better....it's sharper, better built etc, etc.
The Canon L lenses are worth the money, and you could get a 70-200mm f2.8 L IS version 1 for your budget with some change left over.
I could only find a small number for sale used (probably a good sign - they're popular), just a quick browse at some of the reputable places.
If you were willing to nudge your budget up a bit, you might get a version 2, which is supposed to be better still.
Phenomenal lenses....the only way I'll ever get rid of mine is when I update to f2.8....regret not doing it in the first place tbh....but then I am cheap!!
By the way, welcome to TP