Some garages and car-service businesses that do tire changing also offer a tire-storage service. For a fairly low fee, they will simply keep your off-season set at the business. This way, the set you aren't using never clutters up your house; the tires remain in the place where they can easily be put back onto your car when the season changes.
If you have a high enough ceiling in your garage, you can install an overhead rack that will keep your tires out of the way but handy when you need them. These racks can be fairly easily built by anyone with basic carpentry skills, or you can buy a commercial one. The main thing is to attach it very solidly to the wall, because a set of four tires is heavy.
If you have a house with a basement, that may be the best place for tires that aren't being used. Anywhere in the garage besides an overhead rack, they are bound to be in the way, but most basements have at least one corner that will accommodate them. In addition, basements tend to be cool and dimly lit, which are good conditions for the storage of tires, because the rubber won't be degraded by exposure to sunlight.
If you live in a small apartment with no basement or garage, and you don't want to leave your tires at someone's business, you may need to get creative. One way to do this is to make furniture out of your tires. Cut a piece of plywood to a diameter slightly wider than your tires. Put them in your living room, put the plywood on top of them, and drape a cloth over them--and presto, a coffee table.