I'm about 6'1" and a bigger guy myself, and am on my 3rd bike. Maybe some of this feedback will be of use:
1st: 2010 Ninja 250R: Great bike for the handling, but I dwarved it. It did feel a bit cramped at times, but I got used to it quickly. Now I can't sit on the thing without feeling like it's a toy, didn't realize this until I got my next bike, though..
2nd: 2010 Ninja 650R: Definitely felt more "for me" as compared to the 250R, and loved the much-needed boost in power. I found over time though that I was still having issues with back pain, despite both of these bikes having a fairly upward seating position. I often felt that my legs were still a bit cramped, and I found myself leaning more forward than necessary to feel "right" on the bars. I think maybe this bike was a little too "in the middle" in terms of posture between an SS and a touring bike for me.
Current: 2005 V-Strom DL650. This is the bike I'm hoping to keep for a long time, and is the bike I originally intended to get after the 250R. If this bike ever fails or something bad happens, I won't hesitate to get another (newer) one. I'll admit I definitely miss some of the "fun factor" of the 650R with its sportier acceleration and handling, as well as its better looks (face it, V-Stroms are kind of ugly sometimes) but, the V-Strom ultimately suits my riding style better. I do a lot of long rides, and plan on travelling with this bike, especially as it's my only vehicle. So in my case I wanted a bigger bike because of my height/size, but also the functionality of having plenty of luggage space.
Nobody can tell you what the best bike is for you except you, but I encourage you to sit on several at dealerships/shows, and certainly take advantage of any test rides that become available during the season. You might find that for example, you want an SS bike, but find that a sport-touring/dual-sport or even a touring/cruiser style actually fits you better. In any case, best of luck and see you on the road!