I know the area between Alicante and Murcia. I go there about every year, and these are my impressions:
- Good cycling possibilities (Climbs, flats, not too much cars)
-> lots of roads without cars, roads are in really good conditions, a real pleasure. Lots of flats and up/downs, for the climbs you have to search a bit.
To find the best roads the easiest solution is to immediately find a local club: every year an unbelievable number of roads are built and finding a map up-to-date is hard!
Just go out, the first cyclist you meet... just start talking with, he will tell you where to find bike clubs and such. Don't expect people speaking english, but expect them to do the best to understand and help you. (well, most of the time --like everywhere in the world you can find good and bad people)
- Good Training facilities (Swimming, running, Gym)
-> this could be a problem, but depends where you'll live. In the city should not bee too much of a problem. I don't know if living in the center of the city is a good idea with the beautiful small towns you can find there.
- Like minded people to train with
-> *lots* of cyclists there. People are open!
- Reasonable cost of living (rent) ->
life is really cheap if you avoid touristic places.
- Nice winter climate ->
depends... Anyway not too cold. Not hot too...
- Possibilities to study Spanish -> ok
- Proximity to the coast
-> ok (however imho best roads to ride are not on the coast)
- Preferably not the touristiest areas
-> up to you to choose. The city of Alicante is not too touristic, but some places are. You can easily avoid them.
Conclusion: in my opinion, a really nice place to live (and train). Food is good. Lots of cyclists, not too many climbs, you rarely see people with more than 23t sproket. You can find awesome places completely "out of the world".
The sky is often a deep blue that helps a lot beeing happy! :-)
Hope that helps!
Francesco