Check for how easily it starts, check for oily residue on the engine parts. If you can, do a compression test on it.
Check all electrical functions. Hi/ low beam L and R turn signals front and rear, brake light, horn. Test the brakes carefully. Take it for a test ride for sure. If the seller says no rides, walk away. He/ she is most likely trying to hide a problem.
Check the tires for dry rot/ small cracks in the sidewalls and tread. Check tire pressure with a gauge, not by the thump or squeeze method.
If it is a 2-stroke, one of the most common problems with any scooter like that is the exhaust getting plugged up with carbon. You can take the exhaust off of them and literally beat on them (don't dent it all up) to knock it loose and shake it all out.
Honda has made 4-strokes as well. A common problem is the owner not adjusting the valves or doing oil changes as scheduled.
On either engine type, open the fill cap on the transmission and smell it. If it smells acrid and burnt, the clutch will have problems. Check the engine oil on a 4-stroke as well. Brown oil is ok, it just needs changing. Black is bad, it's been in there too long. If it does not smell burnt, the engine might be ok, just change the oil ASAP.
