For what its worth, Marlin makes a number of .22lr bolt actions that fall under almost exactly what you are looking for.
I got my Marlin 917v .17HMR for a little under $250 and I can shoot groups smaller than a dime from 65 yard. Modded the trigger by replacing the trigger return spring with a bic pen spring cut to the same length as the stock spring. Result was a much lighter trigger pull.
The rifle I have looks a lot like the Marlin Model 925. I am very very happy with mine. Will never get rid of it sort of happy.