Quoted:
If you're looking for a bike to ride street with, i would get away from the 600cc sport bikes...
They're not a bike to tool around at 60mph...they shine at twice that and they don't like being dogged around at highway speeds. Their power band is high up in the RPM range which just doesn't suit street riding AFAIC.
I would look into either a larger engine street bike like the gsxr750 or the liter bikes if you want to stick with that look
Otherwise, i would suggest the SV650S or SV1000S for a more street friendly power band and not to mention cheaper initial cost as well.
While it's true that the 600's really come alive past about 9,000rpm, they do just fine below that if you're not trying to be racer boy or attract the local constabulary. I've had my ZX6R for just shy of 2.5 years, and for 10 months of that it was my only form of transportation. Even though I have a truck now, I ride the bike as often as I can (because cages suck, and the bike gets twice the mpg of the truck). My 6R is happy to tool around at 6,500rpm on the freeway if that's what I choose to do with it, though I do enjoy some spirited freeway onramp rides from time to time.
That being said, the suggestion to look at an SV650 or SV1000 is a good one. You'll pay less for insurance, get to use regular unleaded (I think) instead of Premium, and wind up with more usable torque for street riding. They're still plenty fast to keep you entertained, too. Might be something to consider. Also keep in mind if you plant to do much 2up riding. The 600's will handle it, but their suspension is set up for single riding from the factory, and they really lose steam down low. If you do a lot of 2up riding, consider leaving some cash in your budget to uprade the suspension to handle more weight, or consider a larger displacement bike.
As for the R6. I like them as a track bike (based on what I hear, 'cause I've never been on the track). Their performance stats are typical of race-bred mid-sized bikes: they perform much better when you wind them up. Of all the 600's, the newer R6 tends to have the least usable power down low and towards the middle (correct me if I'm wrong here), and while the chassis setup and suspension are scalpel sharp when you're on smooth and fast roads, they tend to be a skoosh firm for general street riding. When you're wringing the heck out of them, however, they're great performers. Many people ride them on the street, though, so it's going to be 100% up to you to decide if you like it or not.
Let us know what you get!