I can't believe nobody has mentioned the M&P22 yet! Mine has been 100% reliable with anything I put through it including the cheapest Wal-Mart bulk box ammo and very accurate as well. It's also nice that it feels and functions like a real pistol being able to use the same manual of arms, holsters and some other accessories my M&P45 uses. I probably should have zeroed in the sights first but this is a 5-round group at 15m fired from a prone unsupported position:
The SR22 is also another good choice, especially for smaller hands. It's about as small and light as the Walther P22 but is made from better materials. Another reliable pistol, mine hasn't been quite as accurate as the M&P but still pretty decent considering its smaller size.
My Ruger Mk-II is easily the most accurate .22 pistol I own and if pure target shooting is your thing, pistols like the Mk-II or Buckmark would be a good choice. However, I find these pistols rather boring and just not a good choice for low-cost dynamic pistol training like my M&P22 is.