Are you after spending a few thousand on a .22LR like an Anschutz? Or are you talking more about run-of-the-mill .22LR's that are really accurate?
I have a Remington 40-X in .22LR that I shoot regularly at 200Y targets with a fair amount of accuracy. I can even use bulk ammo and it's still a really accurate rifle. Has a 26" barrel and as I understand it, they were used by the USMC marksman sporting teams in the 50's and 60's. Got it from the CMP and it has "USMC" marked on the side of it. You can still find them on Gunbroker. Depends on condition, but expect to pay around $2K for a good quality one.
I have quite a few less expensive ones that are still fairly accurate for a .22LR. I like my Ruger Precision Rimfire Rifle. Uses 10/22 mags, is a bolt action with threaded barrel - basically, like a regular RPR, but 80% in size, and in .22LR.