Some really nice .22s out there...
I have been thinking about this question since posted. It doesn't say "favorite" .22 handgun or favorite .22 Target gun or Hunting gun it says "ALL-AROUND" gun and that is where I run into the roadblock to answering.
If one only does one thing with their .22 handgun such as shoot Bullseye then it is a simple matter of choosing ones favorite Bullseye gun. But with each additional discipline one uses a .22 handgun for, such as hunting, teaching, trapping, metallic silhouette competition, concealed carry/self-defense, plinking, hiking/backpacking...the compromises get bigger and bigger.
So this is where I get stuck for an answer as I do all of the above with a .22 handgun from time to time.
Probably the closest I can come is a 4" S&W Model 48 .22 Magnum with the extra Rimfire cylinder. It is accurate enough for Bullseye although somewhat handicapped for Rapid Fire. I can shoot it just about as well long range as a 6" for plinking and MS shooting. With small grips it isn't too heavy or muzzle heavy for teaching new shooters and although I prefer stainless for a hunting/hiking/backpacking like the above Model 63 it would just take a little more care to keep clean.
With new grips...
The second runner up would be a 1911 with interchangeable top ends. A Marvel Longsilde for competition and standard Conversion Unit or for that matter an ACE for everything else...
ACE
Sorry to over-annualized this...Bob