There is a pile of left handed 22s on the market, so here are a few...
For good looking classic looking, Anschutz makes a number of models in bolt action or push pull. Nordic Marksman has a few different ones in stock. You can search for an older Browning T-Bolt or find a new production one. Or search the EE for a CZ 452 American or Lux left hand. I have 2 Americans (one in 22lr and one in 17hmr) and a 452 Lux in .22lr. They are extremely well made and extremely accurate guns. I wish CZ still made then.
The Tikka t1x lh in 22lr is supposed to hit markets here in Canada this year, so that could be an option, but they've been saying for 3 years it's coming, so im not holding my breath over it.
For cheaper bolt actions, Savage makes a couple variations of their Mark 2 series in a left hand but also do one in their B22 series. Marlin has done a number of left handed rimfires in the past, so one of those could also be had.
As for semi auto, I've only ever really come across 2. The savage model 64 which in my opinion is fine for a plinker. But not well made, not accurate and not overly reliable. The other option is one that has just hitter market and its a Ruger model 13001, which is basically a 10/22 custom shop gun that is entirely left handed. I havent played with the ruger yet, but I have plans to buy one for this spring.