At a reasonable price, it is difficult to beat the CZ bolt action .22's for accuracy.
If price is no object, then you could look at the top-end Anschuetz, or older Winchester 52's (which are bid up in part by Winchester collectors), Remington 513's, 37's, 40X, Kimber 82's, etc. But as Bart indicates, there's some deals out there in older Annie's. They shoot very, very well. In general, there are two "families" of Anschuetz .22's - ones derived from the 54 action and ones derived from the 64 action. The 64 family rifles tend to be a bit cheaper, but are still quite accurate.
Consider too that the "second tier" US gun makers made target rifles. There are some Marlin target .22's that were put out several years ago (the "2000" rifles), along with some older Model 35's. Mossberg made a couple target rifles (one that comes to mind was a '144' with Lyman peep sights).
I own both an Anschuetz 1807 and a Win52B target .22. Both shoot so accurately that at 50 yards, if I miss the 10 ring when using Ely-primed match ammunition, I know it was *my* fault, not the gun or ammo's fault. Maybe, just maybe, sometimes I can blame the wind. Maybe if the listener is really gullible I can get away with it. Both of my target rifles have globe front sights and aperture rear sights, triggers down under 1LB, etc.
Open sights are not particularly good sights for accuracy work. At the very least, I'd have any serious .22 equipped with military-style peep sights. Globe sights are great for shooting round bulls on paper, but maybe not so useful for squirrels and such.
The ammunition fed to a .22 is the second place I start helping people improve their results on most any .22. The hyper-sonic, hunting and bulk ammunition types are all terribly inaccurate. The hyper-sonic stuff has never, ever been able to group inside of 3 or 4" at 100 yards for me, regardless of the rifle.
Next thing that matters is the consistency of rim thickness. In years past, people who wanted to improve the accuracy of their .22's with bulk ammo would sort their ammo by rim thickness, then they'd find which thickness closed up their groups and shoot only that thickness of rim, trading off all the other ammo from bulk lots with other people. Today's match .22LR ammo is quite consistent and this tip only works yet with the bulk ammunition types. There's many different grades of .22LR ammo, and the best advice I can give you here is when you have what you believe to be a good .22 rifle, start shooting consistently at 50 yards onto paper, and try one ammo after another, keeping good records. There's dozens of ammos to try. In the Ruger 10/22's I own, I found CCI Green Tag improved results markedly. Your Rugers, being of a different vintage than mine, might not agree with mine.
Last, I'd be looking at your barrel's crown and then chamber. I've seen some .22's with crowns damaged from cleaning. When it comes to .22's, less cleaning is better. You see these guys sawing a bronze cleaning brush through a .22 as tho they were cleaning a stovepipe or something - and that's not helping the barrel.
You can literally pour money into a 10/22 like water down a gopher hole, and for the price of a new CZ, you might be able to make it shoot as well as a CZ. Might. Or you could just say to yourself "I'm going to become a more serious shootist," sell your 10/22 and move up to a more serious .22.
For plinking, 10/22's are a lot of fun.
But when you want to knuckle down and make groups... they're simply not the .22 rifle to own. I honestly cannot remember the last time I had my 10/22's out of the safe. They used to be used as squirrel rifles, then I bought a Savage .17 HMR. Between the Annie and Winnie target rifles and the Savage squirrel gun... the 10/22's (scopes and all) just sit there, unloved, unused, forgotten safe queens. Col. Whelen was right - only accurate rifles are interesting.