By way of a spoiler, I've done my research in this area, and still plan to use PT lumber for framing. That said, I think it's worth mentioning some of the other options. Maybe they are what you are looking for, especially if cost isn't an issue...
Redwood
This is a pretty obvious one. Naturally resistant to rot and termite damage, pretty long lasting. It is more expensive that PT, but it also looks better if you have exposed framing. The stuff for framing is called Construction Common, or con-common. It should be heart wood, not sap wood. A 4x4x8' board should run you about 50% more than you average PT board. Most of what I've read leads me to believe redwood won't last quiet as long as PT. Especially the young growth they sell now. This article from UC Davis
Selecting Lumber and Lumber
Substitutes for Outdoor Exposures says young growth is only moderately resistant to decay. This chart from the article says a lot about the expected life of young redwood:
Acetylated Wood
Of the alternatives, this seems the most interesting going forward. The largest manufacturers seems to be
Accoya and
Eastman. Like a lot of manufacturers, you can't buy direct, you have to try one of the distributors on their website. Not that many listed right now, so you need to see if there is one near you. The big disadvantage is cost. When I heard 3-4 time the cost of PT, I can to kick this option to the curb.
Silica-Infused Wood
It seems like this is a one company product right now, with
TimberSil. I've read a lot of strange reviews about this product. Basically the Silica glass is baked into the lumber, creating a barrier. Some reviews have brought up strange mold and "fur" issues. Also seems to have some issues with distribution on the west coast at least. Worth a look though.