My Gixxer is unsuitable for long trips like this, so we've only taken mom's Kwak Drifter 800 and my step-dad's Kwak Mean Streak 1500. We're doing a three way rotation so all of us get to drive at least one of the bikes before we have to take a shift in the Civic Hybrid. Also my step-dad has recently had back surgery so sometimes he wants to get off the bike.
Mid-size easy riding 600-ish V-twin... it's hard not to recommend my mom's Drifter.
It's extremely comfortable and easy going. Not too heavy. Pleasure to ride. It's an 800, but it's a real pussycat. My 250 Ninja was harder to ride. Kwak has stopped making these but some should be available used.
There are several v-twin Harleys. If that's your thing, have at it. Should be easy to find, too. Only downside is that hogs are expensive. Too expensive, IMO. People are buying a logo instead of functionality. Makes the engineer in me sneer.
Want something sportier? The Suzuki SV650S
has a reputation for being tremendously fun to ride.
That's really all I can think of offhand. Have you taken a motorcycle riding course? I'd definitely recommend it. I think it's the reason I haven't injured myself beyond superficial scratches in ten years of riding.
If you HAVE taken a riding safety course, and aren't totally wedded to the idea of a V-twin, you should give the Honda Interceptor
a serious look. It's what I'll be getting when I become too old and inflexible for a serious "kill you if you're not paying attention every single second" race-replica like my Gixxer.