As with other electronic stuff, you want to keep it away from high moisture (showers, damp basements, etc.). You also want to keep it away from sources of electrical interference, such as large motors. And keep it out of the bedroom if you're likely to be tempted to listen to it all night.

Scanners can be addicting.
As others have noted, some locations may be better for reception than others. This may or may not be important depending on the strength of the signals you are interested in listening to. In more urban settings, many people find that the factory-supplied antenna works just fine. In other situations, you may find it worth getting a better indoor antenna or a separate outdoor antenna. Probably the best advice for that is just to try the existing antenna for a while until you develop a sense of whether or not you're missing much due to signal strength issues.
In some areas, good antenna systems can actually hurt more than they help. Many listeners are finding that nearby pager of cell phone towers broadcast such a strong signal that they mess up reception for other channels.
One final note - some scanners come with various forms of sirens, etc. to indicate approaching bad weather. If you have a scanner with this feature, be sure you don't leave the scanner near pets or babies. When these alerts are triggered, they can get broadcast at a very loud volume that is independent of the volume setting on the scanner.
(Think smoke detector alert volume.)
It would be cruel to have a pet have to put up with that type of noise for a long time if an alert happened while you were not home.