Out walking around - camping, pumpkin patch, b-day parties (outdoors) etc. - Consider picking up a Canon EF 28-135 locally off Craigslist. It's a nice walk-around lens for little money: fast accurate USM, close focusing, and IS. Around here there are usually two or three available on Craigslist for about $200. The reason it's cheap is that a ton have been sold and the market is pretty flooded with them... It was offered as kit lens on 40D and 50D for a few years. But it's not really what you'd call a "kit lens"... it's midgrade build quality and is capable of quite good image quality.There are more than a few pros using the 28-135 instead of the 24-105L (which costs 3X to 5X as much, but is better sealed against dust, has better IS, is sharper at the tele end, however vignettes more heavily at the wide end). 135mm is long enough for a lot of things, though it's best to stop down the 28-135 a little at the most tele end of the zoom (it's a wee bit soft). And, 28mm is merely a "standard" lens width on a crop camera like 60D... So you might want to pair it up with a wider lens (see below).
Canon is now commonly bundling the EF-S 18-135 with 60D... It seems a decent lens, too... We certainly are seeing a lot of good shots being done with it... It's nice that it's 10mm wider than the 28-135... but it is EF-S and it lacks USM. It sells new for about the same as the 28-135, adds about $100 more in the kit than the 28-135 did, and is relatively new so the used prices on it are still about $400.
Another popular standard lens is the EF-S 15-85mm. It's quite compact and covers a nice range for a walk-around lens on a crop sensor camera. And it's capable of very nice images. However, by the time I were spending what this lens costs, I'd be looking for one with an f2.8 aperture (instead of f3.5-5.6), even if it costs a little more. It's EF-S, so also not usable on full frame.
Arguably the "best" standard zoom for your camera is the Canon EF-S 17-55/2.8. IQ is top notch. However, it is rather pricey and "only" covers 17-55 range. f2.8 is always nice to have on a standard zoom, though. Not usable on full frame, though.
I hear a lot of good things about the Tamron 17-50/2.8 non-VC... Affordable and quite sharp. Again, there's limited range and it's not usable on full frame cameras.
Some also like the Sigma 17-50/2.8. It's a bit more expensive though, and another "crop only" lens.
To compliment a "walk-around" or standard zoom, you might want a wider lens such as the Canon 10-22 (if you have plenty of money... it's about $850 new, rarely under $650 used) or Tokina 12-24/4 (new about $550, used around $400). I think those are the two "best value" UWA lenses. There are also Sigma 8-16mm and 10-20 (2 different versions now), Tokina 11-16/2.8, and Tamron 10-24 to consider. The wide lens you choose might be influenced by the standard or "walk-around" lens you have chosen. For example, a 12-24 might match up nicely with a 28-135, or an 8-16 with a 17-55... but an 8-16mm would leave a big gap in some key focal lengths used with a 24-70, 24-105, or 28-135.
If you shoot a lot of portraits, a 50mm would be a nice lens to have. The Canon f1.8 is cheap at about $120 ($150 with the optional hood, if you want it)... capable of decent images, but pretty plasticky and has slower, less accurate AF. The Canon f1.4 is better built and has somewhat nicer image quality (more flare resistant, better contrast, better color saturation, nicer background blur). It will cost $400 US by the time you get the lens hood (necessary with this lens, not mandatory on the f1.8 since it's front element is so recessed).
You don't seem interested in a longer lens, so I'm not going to get into those other than to say that you really don't have to look much farther than one of the four different Canon 70-200s. They are all top notch.
For sake of "full disclosure", personally I shoot both crop and full frame cameras, so my "basic" lens kit is:
- Canon 24-70/2.8 (for its f2.8, L sealing against dust and overall durability)
- Canon 28-135 as a backup/loaner lens, or sometimes as a convenient walk-around lens. (2nd or 3rd copy of this lens I've had, bought used but like new off Amazon for $250, incl. shipping, lens hood & a 72mm B+W filter).
- For wider angle: Tokina 12-24/4 on crop and Canon 20/2.8 prime on full frame.
- For longer telephoto: 70-200/2.8 IS and 300/4 IS
- "Portrait" primes, for their larger apertures: Canon 28/1.8 (mostly w/ crop), 50/1.4, 85/1.8 and 135/2 (mostly w/ FF).
I also use some other telephotos, specialty lenses (macro and tilt-shift), and teleconverters.
Finally, and frankly, I think it's a mistake to buy a lens now based upon "someday... maybe" going full frame. For one, not everyone needs a full frame camera... a lot of people just think it will somehow be the best thing for them. In truth, many might be better served sticking with a crop camera. Another thing, if and when you finally do go full frame, it's pretty easy enough to sell off any "crop only" lenses you acquire. In fact, with prices going up over the past year, you could have bought several Canon EF-S lenses a few years ago, used them, then sold them for a profit now. In effect, you'd have had the use of them for free for the years in between.
There are a lot of excellent "crop only" lenses available, they can be more affordable, more compact and perhaps even a better match for your current camera. It would be a shame not to seriously consider them.