I had a Honda CB350 as my first "road bike" last year, so while not exactly the same as the 360, they're similar. Was a fun, light, nimble bike, but the vibration was definitely annoying on the highway since my work commute is 14 miles each way at 65mph. For just bouncing around town though it was a delightful, solid little bike, and it really got my feet wet. My 650 is definitely "heavy" by comparison, but is much, much nicer at highway. Oh yeah, the fairly low seat height is nice too for "the short people". Damn 30" inseam....
Anyway, finally sold the 350 this spring to a coworker as her starter bike. She's been riding it almost daily to work since then.
350 In short:
+Light, Nimble, Handles well
+Breaks stop decently
+Peppy at low speeds
+Low height so more confidence for new riders
+Very nice sound from the twin exhaust
-Vibration is a pain at highway
-Mirrors tend to buzz unless you get some really wide FOV ones
-Carbs can be finicky, and idle has to be set individually
-Fairly cold blooded