I do 3 things to the 10/22s I buy.
1. Fix the trigger. Last one I had, the trigger was really bad. I fixed mine myself, but there are drop in parts that will do it quicker.
2. Do some VERY simple action bedding so that the action isn't loose in the stock. Doesn't have to be fancy, you just want the action to fit in there and not wiggle around even without the screw and the barrel band installed. Usually you can put three decent sized spots of some kind of thick glue in the stock around the receiver, one in back and one on each side. Then put some plastic wrap over the spots and install the receiver so it squishes the glue into place. Put enough plastic wrap on the spots so that the glue doesn't squeeze out around the edges and glue the receiver in place. Don't get carried away with a ton of glue and watch where it's going to impinge on the receiver to make sure it's not going to lock the receiver in place--don't put it where there's a lip or a hole in the receiver. Once the glue and plastic wrap are in place, push the receiver into the stock and install the stock screw. When the glue is set/dried, you can take the receiver out of the stock and the plastic wrap will usually just pull right off the glue. If not, you can trim any excess plastic wrap.
3. Do something about the front barrel engagement. It doesn't need to be free-floating, but it needs to be tight so nothing shifts around up there. One way is to make sure that the barrel band fits the barrel tightly and is tight on the stock. You can do this by putting a layer of tape inside the barrel band before you install it so that the barrel won't be slipping/moving around in relation to the band and so that the band won't move on the stock at all. Or you can leave the barrel band off altogether and put a self-adhesive felt furniture pad inside the barrel channel at the front of the stock to put some upward pressure on the barrel and keep it from bouncing on the stock when the gun is fired.
I've never had any issues with accuracy after those changes. Costs me some time and maybe a few bucks of materials. Last one I did, I reworked the trigger with a flat surface and a couple of grits of sandpaper so I didn't even need stones or files.
You could check the crown to see how it looks after shooting. If the carbon pattern on the muzzle is symmetric, it's good. I don't remember ever having to touch up the crown on a 10/22.