Helps to get a reply from someone with personal experience. I'm 6'4", 260lbs and I've been enjoying the Ninja 250 for the past 7 years (though I started riding 20 years ago). You'll look big on it, but you'll look big on ANY bike shy of a BossHoss. The 2008+ changes made the 250's much less comfortable, I kept mine for less than a year before selling it to buy a 2005.
Even with your size, it'll hit over 90mph, be able to cruise the interstate at the speed limit with plenty left for climbing hills, at higher than 5000' in elevation, into a headwind (like, across I-80 in Wyoming ~ again, which I've done), or go play at the racetrack. Part of the fun with the 250 for me is that the bike feels like a toy. SO easy to toss around and have fun on... probably why its been the only constant in my garage over the last 7 years. It's actually been my only streetbike for the past 3 years, when I sold my YZF600r (boring to ride legally).
Rest assured, the bike will not only be fine, it'll still do Everything anyone could ever need a motorcycle to do.