This scope does not have the magnification you ask for but it is very durable. I finished deer season with a simmons eight point 4x fixed power scope mounted on a 12 ga. The inexpensive scope never budged under the intense shock produced by a 12 ga 3" slug. I got a regular shotgun scope after deer season and put the Simmons on my Marlin XT 22MR. You will be hard pressed to find a more durable scope at any price.
I have Bushnell Sportview 4x12x40 scopes on a couple of my 10-22's. They run a little under 100 bucks. I bought a couple used a few years ago for 30 bucks a piece (I love the court days festivals in Ky!) that I just love. I think they run around 70-80 bucks new. They are clear and pretty sturdy and I really don't like spending big money on a 22 scope unless I'm building an uber bench 22. I like the adjustable AO and the allow my old man eyes to make a pretty good shot out to 175 yds. There are better optics out there bu tit's really hard to argue the cost vs performance on these scopes. I vave a couple of the 3x9 Bushnell scopes that seem pretty good too.
If I wasn't going to use what I have I'd probably get a Nikon,
The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants. Thomas Jefferson
Nikon Prostaff is what I use on my Savage 270. Great scope and inside your price point. I have a couple $60 -$70 Walmart type scopes for my Savage 22. They work just as advertised. My Riger 10/22 I prefer to use the iron sights.
Unless you are going the hi end ammo, trigger, bull barrel route, any mom and pop scope should suit a plinker.