When I got my 60D, I was still using the 18-135 lens I had be using on my 30D before. A good lens, good results, and handles everything from relatively wide-angle (for cramped quarters) to a decent telephoto to 'zoom in' on what you want to zoom in on.
The problem is that it is not a 'great' low-light lens unless you add an external flash. The f3.5-5.6 sounds like its great, but the f-stop 'range' indicates it changes from f3.5 to f5.6 while it is zooming from 18mm to 135mm. If memory serves, I read somewhere that the older version of the lens I had was f4 by the time it was 25mm or so, and f5.6 by about 50mm, give or take.
Meanwhile, the 70-200 f4L retains its f4 throughout the entire zoom range. But in low light, f4 does have its limitations. I have a 24-105 f4L IS. In most cases, increasing the ISO on my 60D to 2400 or even 3200 allowed me to keep reasonably fast shutter speeds to stop action. But that wasn't always the case. Sometimes I had to slow the shutter speed down to the 1/10th-1/40th range to get an acceptable exposure, even at ISO 3200 (a bit noisy, but correctable in post processing). But at those shutter speeds, the non-blurred-subject 'keeper' rates was in the 1 in 25 or so at 1/10th. So, a flash is still required in many situations.
As Big Mike suggested, perhaps a third party 70-200 f2.8 with IS (or its equivalent) might be a good choice. But then, nothing says you have to buy 'new' only. Check out the used portions of
B&H Photo,
Adorama, or
KEH camera (all very reputable vendors) and you might find a very good condition Canon 70-200 f2.8 IS within your price range.
But the 70-200 on your 60D is really 'too long' (too much telephoto) for indoor shots in your house. In a banquet hall of any size, or outdoors, it's a great range. Getting the 70-200 -only- would severely limit your shots with the subject nearer than, say, 25 feet. That's where the 18-135 'shines'...it's jack-of-all-focal-lengths capability. Close, medium, and far, all pretty good....at the 'cost' of not-so-great without a flash indoors.
So, I'd like to propose two possible solutions...the 18-135 + an external flash (the popup flash is good for perhaps 10 feet, and that's it!)
or, the 70-200 f2.8 (any brand/new/used) + a 50mm (or 35mm) f1.8 or f1.4 lens for indoor work. But...just because the 50/35 can -do- f1.8, the tradeoff is very thin depth of field (plane of acceptable focus).