.17hmr
I'll second Sir William on the .17 HMR. While it offers some unique small game/varmint opportunities from a rifle, the shorter pistol barrel robs it of it's velocity, which is it's chief advantage.
.22 WMR is another round that, in my experience, has been better suited to rifles than to pistols. Your mileage may vary.
It seems to me that .22 LR is a good multipurpose round that can be very effective for a variety of applications. It is useful and accurate in a pistol, chances are you have ammo lying around, and it can be had most anywhere. A single action .22 revolver can be a fun, accurate, and highly reliable firearm. While there is much to be said for some of the higher priced firearms, I have had good luck with EAA products in the past. I have also had nothing but good with my Heritage Arms "Rough Rider" .22 single action. They can be had inexpensively and generally include an interchangeable .22 Mag cylinder. I have a blued/casehardened one and would suggest the same. I have heard that the nickel finish is not terrribly durable and will sometimes flake or chip.
Hope that helps somewhat.