The first thing that would come to mind is the little Chipmunk .22's; right around $170 new, but i've seen them as low as $100. They're accurate, simple, safe, compact, and light weight. The nice thing about them too, is since they are youth sized, you can use it to teach the little ones to shoot. Here is a review on them:

http://www.gunblast.com/Chipmunk.htm

Now, if you're looking for an adult size .22 then you might have to bump up your price range a bit if looking to buy new.

For an inexpensive bolt action .22 I like the Marlin 981T. It's a tube fed bolt action rifle with a 22" inch barrel and synthetic stock. The nice thing about being tube fed is it can use .22 shorts, .22 long, or .22lr ammunition; and because it's bolt action it's very reliable and it can be rendered very safe (take the bolt out and lock it up separate). It also has iron sights, as well as being drilled and tapped to be able to easily accept a scope. Price is right around $200 msrp.

Finally, the old standby, the Ruger 10/22. It's a bit more expensive than the other two options, but it's semi automatic with a removable magazine. This is probably the most common .22 people buy and it has a huge aftermarket. It can only shoot .22lr though, and it prefers higher velocity ammunition to properly cycle. Basic model is around $250 msrp, but you can find typically find them for less.

All are fine choices depending on what you're looking for.