Given the amount of time going from 55nm to 40nm (HD4xxxx to HD5xxx) and assuming the HD6000 series is a refresh at 40nm, I'd guesstimate the HD6000 series would be scheduled for a Q4/2010 release, but end up being pushed back to Q1/2011.
According to a source cited on Wikipedia, if the HD 6xxx series does turn out to be the Northern Islands family, which is not going to be a refresh for the HD 5xxx series, but an entirely new family of cards, the release was originally slated for late 2010/early 2011. There hasn't been any sort of official announcement about architecture, release dates, or other timeline, and so right now all we have is an entry on an ATI roadmap from 2009. Whether or not that will play out as they expected back then... Well, only time will tell.
This site has pictures of the official AMD announcement identifying Northern Islands as the next line of cards for ATI, with a projected 2011 release date. In the presentation, the cards were identified as 32nm, but it is rumored that ATI will be skipping 32nm chips, and that the HD 6xxx series will be 28nm. http://plaza.rakuten.co.jp/moemaid/diary/200910310002.
Make of it what you will. Fingers crossed for a more official announcement soon!
E: As an aside, I'm assuming that the HD 6xxx family will be Northern Islands, and not the rumored Southern Islands family, which is supposed to be a refresh of the HD 5xxx family with some of the elements of the unique line of Northern Islands cards. The Southern Islands cards, as another poster noted, are rumored for launch in the second half of 2010. Hoping for updates soon!
Well, I also read on wikipedia that ATI has plans on doing minor refreshes every 6 months and major releases every 1 year after a major launch. So, SI which is a refresh should be launching this year around October while NI, which is supposed to be new architecture would be launched in Q1 2011. That is what I guess.