Tourist Trophy for PS2 has scooters! And not a facsimile of a scooter like the Faggio (pronounced FAH-jee-oh) in the Grand Theft Auto series.
TT is produced by the makers of the Gran Turismo series and is modeled very much like the latest version, GT4. While it has no Vespas in it, there are a few Aprilias - haven't gotten that far in the game yet to know what models.
The first bike that's in your "Garage" is a Suzuki Skyway. Also available are scooters from Honda and Yamaha.
The GT series was a cakewalk for me driving cars, but motorcycles are a bit harder.