You are a perfect candidate for a Yamaha V-Star 650. It is a larger version of the Virago 250, and has enough power to take you anywhere you want to go. It even has shaft drive. And best of all, it can be had for a very reasonable price.
But I have to admit I don't understand your aversion to the Virago 250, IF you fit on it. I have a Goldwing, and still put 20,000 mostly highway miles on a Honda 250 Rebel, just for fun. I find traveling on a small bike to be a blast. I only sold the Rebel because I was to big for it, and it wasn't all that comfortable. I am currently looking for another 250, and plan on giving the Suzuki GW250 a chance before buying anything else. I have also had several 125-150cc scooters, and still have 3 of them, including a Yamaha Vino 125 that I put 24,000 miles on. If you like the riding position of the Virago, I would definitely stay away from any type of sport bike. Their primary function seems to be some kind of torture device.
I won't spend more on a bike than I think it's worth, but if it's a good deal, I don't seem to have a problem buying bikes I don't need.
2002 Vulcan 750, 2013 Royal Enfield B5
2001 XT225, 2009 Genuine Stella
1980 Puch moped