How much weight and size will you put up with?
To add yet another vote for the same bike several others have already suggested ... Everyone that I know who has a Yamaha FJR, and there are a few, loves them. And they don't break, and although they weigh something, they're not horrendously heavy - and they can be made to hustle. And they'll carry a passenger without issue, and they have luggage available. Cruise control, heated grips, etc.
Personally I prefer something smaller and lighter. So far, my preferred motorcycle to rent while on trips is the BMW F800ST (older models) or F800GT (which is what it's called more recently). I also had their cousin the F800R, the naked one with no fairing, basically the same bike otherwise. Has side luggage and top box, although they're smaller than on the big-rig touring models ... but then the bike is a lot lighter and can be chucked around more easily. Honda VFR800 is about the same size and weight. But it seems like BMW really supports the rental outfits, particularly in Europe and Australia. I'm not sure I'd buy any of these, but they've been good rental bikes.
My recent experience with a rental adventure bike, BMW F800GS (Cousin to the bikes listed above), turned me off that segment. Too high, too tippy, too soft, and despite how high the bike is, cornering clearance when riding on pavement was inadequate because the suspension was so comically soft that it simply flattened out too easily when cornering, grounding the center stand at what I would consider a moderate pace. Not for me. I suspect that carrying a passenger would have it on the bump stops.