I've travelled on a plane once with a uke, and from the experience, I think I'd stick to the following rules:
1) Tenor or smaller. I took a tenor in a hard case, and I don't think anything larger would fit in the overheads. Maybe a baritone (which is what I'd like to take) would fit with a gig bag, but that leads to...
2) Use a hard shell case. They like to stuff those overhead bins as full as they can, and neither the flight attendants or your fellow passengers will be on the lookout for a (possibly) expensive instrument. Also, you might get asked to check your case at the gate. If this happens, in the advice I've been given by other musicians, smile and thank the staff, accept the ticket for the check-in, and then rip it off in the airway down to the plane... then carry it on like nothing ever happened. Feign ignorance if caught, and be glad you got a hard case.
3) Finally, don't take an instrument you can't easily replace. This really sucks... you want to take your nice instrument with you on vacation, right? Now you gotta leave the thousand dollar Kamaka at home and take your cheapie Kala. Oh well. If it breaks, at least it's not the end of the world. You always have the nice instrument at home.