Abruzzo can be broadly divided in three parts:

-the coastal area, which is the only one heavily urbanized in the region and the only one when you can move around without a car, but it is simply bland and uninspiring;

-the hills, where you will find your average Italian hilltop town with good food, friendly inhabitants and romantic views on the sea and the mountains. This area is probably what you are looking for but there are better hilly areas more north, like in Umbria or Le Marche.

-the inner mountainous area, around L'Aquila, which is by far the best when it comes to scenery (absolutely breathtaking), nature and air quality. It's also great for any kind of outdoor activities such as skiing or hiking, if you're into that kind of stuff. You have to keep in mind, though, that the towns outside L'Aquila area are quite remote, have no cultural life to speak of and public services are lacking, especially when it comes to public transportation. They are also still recovering from the 2009 earthquake; in L'Aquila, which before the earthquake had a nice college town vibe, some parts of the city center are still closed. Also, since the towns are full of elders, you might have a hard time trying to integrate if you aren't really fluent with your Italian. My advice is to avoid smaller towns and concentrate in the larger ones around L'Aquila, Sulmona and Avezzano, and in the more touristic places.

Rent prices shouldn't be a problem anywhere in the region, but housing is definitely less expensive in the mountains except for the ski resorts- Rocca di Cambio, Ovindoli, Pescasseroli, Roccaraso, Scanno.

About the weather, I dunno your preferences, but the climate of the inner areas might somewhat resemble your hometown's (four dinstinct season, warm summers, cold snowy winters - make sure to have a good heating system) while the climate on the coasts is milder and sunnier.

Long story short: it's a very rural area, if you don't count the coastal parts (but there's no particular reason to pick those). If living up in the mountains is your dream, then Inner Abruzzo is what you are looking for and you may need some more advice to pick the best town. If you are looking for a picture-perfect Italian medieval town on the hills in a gentle landscape, then Umbria or Le Marche or even Lazio are better.