For around $200 or even a bit less, you can get a really nice scope for a .22LF.
Forget about Simmons and Redfield. Take a look at the Bushnell Elite 3200 (which is at the upper limit of your budget, but still within $200). For a less expensive scope, look at the Bushnell Legend, or even the Bushnell Trophy - again, all within your $200 budget.
You can also take a look at the Nikon Buckmaster, which is about the equivalent of an Elite 3200 - both price wise and quality wise.
If you want to take a look at exact prices on exact models, then go to
www.theopticzone.com. I have bought quite a few scopes from them and I have been very pleased.
Zachary