If you want to go really cheap, but still accurate, try a low-end Savage. I believe they still make a bolt action called the Mk II (when I bought mine about 15 years ago, it was called a Lakefield Mk II, made by Savage).

It's a bolt-action .22 with a curved, 10 shot detachable magazine, and it's uglier than sin on top of looking and feeling cheap. However, it was the most accurate .22 I've ever had. With several types of ammo I could shoot into one ragged hole at 25 yards and quarter-sized groups at 50 yards. I can't count the number of groundhogs I shot with that gun when I was in high school - from ranges of 10 - 80 yards, mostly head shots.

I think you can pick one up for $125 or so, then spend a little extra on a good scope, and you're good to go!