A motorcycle will give you 17-18 inch wheels. If you are good with 15 inch wheels you can choose a number of scooters now available.
There are a very few exceptions in between.
Piaggio owns many brands of scooters and motorcycles. They produce Piaggio, Vespa, Gilera, Aprillia, Moto Guzzi, Derbi, and Scarabeo.
So you have some choices.
If it's the style of the body work then you may be stuck with Vespa or something that is similar in design... and the 12 inch wheels which is the standard on that platform.
Another option would be the Kymco People S150 which has 16 inch front and 14 inch rear wheels. There are others as well like this.