Regarding AF....
Autofocus in 5DII is not better than 60D's overall. Some might say it's not as good. At the very least, the AF systems are different, more tailored to each camera's basic design purposes or goals.
5DII has nine visible and selectable or usable AF points, same as 60D. However, on 5DII, only the center point is the more sensitive "cross type". All nine points in 60D are "cross type". This makes the outer points on 60D more generally useful.
Something the 60D doesn't have, the 5DII has six additional "hidden" AF points clustered right around the center one that can be turned on or off optionally. However, they are only effective in AI Servo mode, so are used to help the camera track moving subjects. Even so, 60D is better at tracking movement than 5DII. Of the subjects you mention, perhaps only kids are a relevant and possibly faster moving subjects.
5DII autofocus also manages to focus... though it will do so pretty slowly... at about 1EV lower light than either 60D or 7D. That might be relevant when shooting street life in low light situations.
7D has the much fancier 19 point AF system. All 19 points are "cross type". In addition, the camera has a dedicated AF processor, similar to 1D series cameras. That makes it very good at tracking moving subjects. This and a few other upgrades mostly for "sports/action/pro" shooting are what you pay the extra for, when you buy a 7D.
If you have trouble getting good focus results with 60D, which is an easier to use, more simple and straightforward design AF system.... 7D would probably be very frustrating. 5DII would be more familiar, though will generally be a little slower.
Concerns about image quality...
You would see no gains going from 60D to 7D. They are identical when it comes to IQ. And with good lens, skill and proper post-processing, you would have a hard time telling either of them apart from 5DII images, unless making really large prints from them.
Straight from the camera, images from 5DII appear sharper. But that's just because the crop sensor cameras have to use strong anti-alias filters that make their images appear softer initially, but when sharpening is properly applied they will have nearly as much fine detail.
5DII is ideal for a landscape photographer who is going to be making very large prints. But a 60D or 7D can nearly equal it, with good lenses, skill shooting and proper post-processing of your images.
5DII does offer slightly greater dynamic range, meaning it can retain more detail in highlights and shadows, compared to the crop sensor cameras.
5DII also is useable about one stop higher ISO than 60D or 7D, will give lower noise in images at high ISOs. This is just the nature of a less crowded, full frame image sensor. For example, where I'll use 7D to 3200 without much concern or need to spend a lot of extra time on the images in post-processing, I will use 5DII to ISO 6400.
Built-in flash...
5DII doesn't have one... 60D and 7D both do have one. A deal breaker? Really?
In my opinion, built-in flashes are a joke. They are anemic and located in the worst possible place for nasty redeye, ugly shadows and even can be partially obstructed by some lenses. If Canon offered 60D or 7D without a built-in flash for $3 savings, I'd take the savings over the flash. I have 9 Canon cameras with built-in flashes and can count on one hand the number of times over the past ten years that I've actually used them. An accessory flash is much better option... far more versatile and powerful... giving much better results. Modern ETTL flashes are super easy to use, too.
You already have an accessory flash... I'm not sure why you'd consider it a deal breaker or not, if a camera has a built-in flash.
FPS...
Is pretty meaningless for most of what you say you shoot. Kids might be an exception on occasion.... but your current camera can shoot 5.3 fps, as fast as or faster than the 5DII and most other DSLRs & 35mm film SLRs ever made, though not as fast as the 7D.
For the purposes you mention... These three camera models break down as follows:
Portraits: 5DII best, 60D 2nd best, 7D 3rd best.
Landscapes: 5DII best, 60D 2nd best, 7D 3rd best.
Kids: 7D best, 60D 2nd best, 5DII 3rd best.
Street/low light: 5DII best, 60D 2nd best, 7D 3rd best.
Note: I rank 7D lower than 60D in many of these cases only because it costs more, but nothing is gained, image quality will be pretty much equal.
However, looking at the small portfolio of images you have posted, I would ask how much have you worked with the 60D? Is it the first DSLR you have used?
I do not think you need to be considering a different camera, but learning how to get the best out of the one you have. There are some things you might want to do. For example, some of your shots might have benefited from using a circular polarizer, such as shots of water where there are reflections. Another thing you might want to try is the EF-D focus screen for your camera, which has a grid on it to help keep horizons level, buildings vertical and arrange compositions. Also, many of you images look super saturated... I am not sure it that is intentional or not. Maybe it is. If not and if you don't already have one, you might consider a graphics quality computer monitor and a calibration device for it.
Those are just a few ideas, things that I think would be money far better spent than changing cameras. Other things... take some classes in photography, read some books on photography... join a local photography club and go shoot more. All these will likely give you far better return with the camera you already have, than switching camera models now.
If your photo numbers are sequential, you appear to have taken less than 2000 images with the 60D (Heck, some days I shoot more than 2000 images, average about 50,000 a year). I really think you need to spend more time with the camera you have and exercise some patience.
Henri Cartier-Bresson said "Your first 10,000 images are your worst." But that was back in the days of film. With digital cameras that promote thoughtless snapshooting and high frame rates, the figure today is probably closer to 50,000.
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