Motion.
Yes PM me with questions. also I can give you my Skype if you want to chat about the different options.
I agree with Jordi about the area between Valencia and Alicante. Look up places like Altea, Javea, Denia, Calpe. Those are directly in the coast. If you go too inland in that region the weather is colder in winter (high 30s in february).
altea - Google Maps
My family comes from that region (look up Alcoi in the map above), so I have direct experience about the area.
US$ 2000 is more than doable. Even US$1000. Even US$800. You can navigate
www.idealista.com to explore the areas and prices. Idealista is the largest housing website in Spain. Here are some examples:
http://www.idealista.com/pagina/inmueble?codigoinmueble=VW0000004020325&numInm=7&edd=list
http://www.idealista.com/pagina/inmueble?codigoinmueble=VW0000000636500&numInm=10&edd=list
http://www.idealista.com/pagina/inmueble?codigoinmueble=VP0000004695357&numInm=9&edd=list
http://www.idealista.com/pagina/inmueble?codigoinmueble=VW0000003894920&numInm=12&edd=list
If you want to stay just a few months look for "vacation rentals" in the site. You could take advantage of low prices in winter and stay 1 month in each place!!!
Although I am partial to the area above, you should also explore Andalucia, especially if you go say 50 km inland. Explore the area between Ronda and the coast:
http://maps.google.es/maps?q=ronda&oe=utf-8&rls=org.mozilla:es-ES
fficial&client=firefox-a&um=1&ie=UTF-8&hq=&hnear=0xd0d314685035fad:0x9b8879fb40db634,Ronda&gl=es&ei=qoSlToCfFZPS8QOe18zbDA&sa=X&oi=geocode_result&ct=image&resnum=3&ved=0CFEQ8gEwAg
I do not have direct experience in the area, but it attracts retired foreigners while still maintaining its character. I warn you that the accent is very think in that area.
If you decide to come to Madrid I can show you around and maybe help you with your planning. Also I can help you during the process with translations, negotiations with locals and so on.
BTW, as soon as you get off the plane get a cheap prepaid phone to help you contact hotels, landlords and such.
Shoot your questions!!!
Saludos