Thinking dry country for your asthma based on loml experience and my own.
The main caveats are:
We do have some unpleasant plants out here in spots so it would be good to check if you're allergic to them. Usually they only bloom for a few weeks but when they do boy howdy! The worst are ragweed and rabbit brush, but done of the introduced plants like olives are really bad as well. Some spots are worst than others, where we're at now we get a bit of grass, oak and pine pollen in the spring but then it settles down to not to bad the test of the year. We're in a valley though so it's dark for four months in the winter which gets pretty old.
Avoid valleys. They fill up with smog or inversion layers in the winter and dust, smog, and crud in the summer. Places like Phoenix, LA, or Salt Lake are not asthma freindly (some of the hillsides around them are OK, but the valleys are horrible).
Hawaii was pretty good, on the dry side of the island. Especially up the hill a bit with the windows open all the time and the breeze blowing through The wet side had enough mold and mildew to set either of us off after a few days. The dry side wasn't so good in closed up buildings either (it's dry in rainfall but still has plenty of humidity). The price of everything kind of ran us out of there though.
Love thy neighbor, yet pull down not thy hedge.