I'd suggest basing your plane at Jacqueline Cochran Regional Airport (KTRM) in Thermal, CA. Here's how it does on your criteria:
1. Palm Springs has lots of outdoor recreation, including hiking, Joshua Tree nearby, easy Mooney access to various ocean/lake cities and national/state parks, numerous golf courses if that's your thing. You are also just short flights away from Catalina Island and Big Bear Lake, which offer opposite ends of the weather spectrum but are rich in recreational opportunities. There's Santa Barbara and Paso Robles wine country (Temecula Valley is even closer), beach destinations in San Diego, Santa Monica, Santa Barbara, and more, and Northern California's lush forests and redwoods are also within a day's reach. Pretty much anything you could want outdoors can be found a Mooney ride away. When you want to get out of California, there's Arizona and the Grand Canyon, Utah, Colorado, Nevada. You can fly to Las Vegas for the weekend on a whim, see a show, and be back in no time.
2. While you'd be in California, and thus would pay California property taxes, the prices for Coachella/Thermal/Indio-area real estate are much more reasonable than you might think, and certainly more affordable than living closer to Los Angeles or San Diego, let alone the Bay Area. If you wanted to spend a little more for luxury you could look in the Palm Springs/Palm Desert/Indian Wells zip codes.
3. Palm Springs International is maybe 30 miles away, Ontario International is within an hour's drive, and LAX, BUR, SNA, and SAN are all within reasonable driving distance for direct and connecting flights. Lufthansa has a major presence at LAX; I see their giant A380's running back and forth to Germany out of LAX every day.
4. TRM is a growing airport with plenty of undeveloped space; there is a great opportunity to build and own your own hangar. I can't speak to the current existing structure availability but it'd probably be very reasonable to buy and build on the field, and end up with exactly what you want.
5. I've always been treated well when visiting Thermal/Palm Springs. The local municipalities and politicians proudly support airport development. A lot of investment in Jackie Cochran Regional has sprung up in the last several years. There's been some talk it may eventually get an FAA tower but for now it's uncontrolled.
6. Tons of universities in the LA basin alone, including UCLA, USC, Loyola Marymount, UC Riverside, Claremont, and the universities in San Diego are also close by.
7. Warm, desert climate. TRM is actually below sea level. Density altitude is a factor to consider when it's hot but all of the airfields in the Palm Springs basin have long enough runways to compensate (TRM's 17-35 is 8,500' while 12-30 is 5,000'). Wind can pick up and gust in the afternoon, but the mornings are more sedate. I've visited several times and only had gusting winds once, and they were quite manageable thanks to TRM's choice of primary and crosswind runways.
8. Longer flights to Germany than the southeast, there's no denying that, but LAX is close enough for convenience and you can get direct flights on Lufthansa. People complain about the traffic, but it's more than manageable if you plan ahead and schedule accordingly. On days when you just can't stand the traffic, Santa Monica (KSMO) and Hawthorne (KHHR) are there as options for Part 91 "connecting" flights to LAX.
With all that said, maybe Palm Springs just doesn't work for you, but in my humble opinion there's a lot of potential for an aviator's retirement destination.