My son's boys don't have scooters but their bikes are stored in a garden shed.
If you don't have such facilities I would say the best way to store them for easy access is in a rack, that is made for them. They could also be hung on hooks on a garage wall

Bike racks are best for easy access -- and the easier to get to, the more they will be used. But you do have to worry a bit about pinch flats with some rack designs. If you get a floor rack, get one that has fat poles and is designed like the ones you'd see in a public bike rack on a street.

A basket mounted on the wall nearby for helmets & stuff will also be handy.

One option: the RazrRak scooter stand. This is cool! It will keep them standing up, or you can mount it on the wall.

Amazon.com has a good price on it, and Organize.com sells it as well (good pics there)

Here's a similar stand from the Razor company, but it doesn't hang on the wall.
http://shop.razor.com/Razor-and-reg-_Kick_Scooter_Stand/

I know there were other types.

Here's a rack for scooters AND bikes--if you've got floor space in the garage, porch, or backyard, this actually looks good!

http://www.youtube.com/watch?v=CDuerO0kF_o

http://www.scooter-stand.com/

Here is a link that might be useful: RazrRak scooter stand

I have this problem, also - with the added complication that DS's scooter is electric! I'm told that it can't be in freezing temps, so what do I do over-winter? (Only garage is far from house & gets well below freezing).

Anyone have ideas?