There's another kit lens option you could consider, which some people prefer to the 16-50mm that comes with the A6000 - pick up one of the older 18-55mm kit lenses that came with previous NEX models. It's a debate how much better or same it is, but some at least seem to feel it might have been a slightly better overall lens, and it's not an extending/power zoom type lens, which some people like myself just can't stand (the lens auto-retracts all the time when you're not shooting, takes longer to extend again on wakeup, and is just slower in use with the zoom switch rather than a nice old twist of the wrist). You can find them everywhere very cheap - $100ish - and pick up the A6000 body only. Also, some have indicated Costco was selling a bundle A6000 that included the 18-55mm and 55-210mm lenses, rather than the usual 16-50mm...that's something else to look for.
Remember in all the reviews of 'bad' lenses, much of the time there's a combination of very very picky, high-end pixel peepers comparing much more expensive lenses and decrying that the kit lens is horrible, and others who just keep quoting that the kit lenses are unusable based on no actual personal experience. While the kit lens isn't a low light monster, isn't a depth-of-field master for shallow closeup work, and isn't a speed demon; for normal, every day walkaround shooting for a majority of non-professional photographers who won't be needing to make 5-foot prints, the kit lens is just fine. Despite two camera systems and 30+ lenses, I still routinely use my 18-55mm kit lens on my A6000 for Disney, for cruises, and for general walkaround stuff, and it does just fine. You can always look to upgrade the lens sometime down the road if you really want to go to something better...save up and spend bigger money for something like the Zeiss 16-35mm F4, or who knows what's coming down the pike as Sony has roadmapped 8 more lenses coming over the next year or so, one of which might be a faster standard zoom. Just something to keep in mind.