In that price range there are two excellent choices that I've used with great success.
First look at the "Simmons 3-9X32 .22 Mag." scope with Adjustable Objective (A.O.). I've got two of these and they have served me well for quite a number of years. Price ranges from $45 to $65 depending on finish and sales available. I've even seen them as low as $39 before.
A year or two back I decided to scope my old Remington 512 bolt-action .22 rifle and went with a Walmart "CenterPoint 3-9X32 .22 Rimfire" scope that was availabe locally for $54. It has been a remarkably good scope. It's clear an precise through all the power ranges and has held perfect zero since I set it up. I really like the mil-dot style reticle. I zeroed the rifle at 50 yards (typical) and then all I have to do to be on target at 100 yards is use a two-dot holdover.
As has been stated, do yourself a favor and spend another $10-$20 for a good set of Weaver or B-Square rings. It'll be well worth the extra cost.