Its interesting that after 4 dozen or so posts, nobody has actually addressed that need. Take a look at
Rossi Wizard

MSRP is less than $400

My favorite is a Remington pump, model 572. Also have a Marlin 39A. Both are wonderful shooters.

Got around a half dozen 10/22 in different configurations and may well have fired more rounds out of 10/22s than any other platform. With good magazines, they can function very well. Lousy mags cause FTF or FTE or other failure that ruins the experience. Metal feed lips on the mags seem to be the biggest factor as Ruger's new 25 rounders work great. Extractor tuning can be a bit of trouble in the event your particular 10/22 has extraction issues. Easy to fix and well documented.

One of the biggest problems with 10/22s is what everybody else says is so good about them - so many parts/options/choices one can EASILY end up with a $1,200 22LR built from top-shelf parts. Ouch. Tackdriver, maybe.

The S&W M&P15-22 has, in my personal experience, been a more reliable platform than any of my 10/22s. All your AR goodies will fit right on - move them back and forth between your M4 so you don't have to buy 2. The Ruger SR22 is a heavy option. I prefer the M&P15-22.

Dedicated upper for an AR you already have is a nice option. If you are going to buy a 10/22, I'd recommend the "Compact" model as it has a desirable 16" barrel. One setup for my wife has the 16" barrel and a Blackhawk adjustable stock - superlight setup adjustable from kid length of pull to full size!

I do not have a bolt action 22LR as I move up to 22WMR if I'm going to go bolt action...