Well, my advice to you is to go on last.fm, get on the last.fm radio, type in a genre you're interested in then listen. It's reallllly not a good idea to label western music as generic, there's a huge variety!
I mean, even though Madonna is quite generic these days, her older works are amazing, listen to her album "Ray of Light".
Some western artists I enjoy are:
Alanis Morissette (her latest album "Flavors of Entanglement" is very interesting to listen to), Catatonia (they've split up now, but I love their album "International Velvet"), Émilie Simon (if you like Kanon Wakeshima, you'll love her voice), Juanes (he's really charismatic and he's talented! I recommend his album "Mi Sangre"), KT Tunstall (She's very bluesy and rocky, I love her!
), Lisa Mitchell (her debut album is the best I've heard from Australia LOL), Kate Nash (you might not like her, but her lyrics are undeniably true to life! ROFL), La Roux (they're quite popular atm, they're quite good..), McFLY (they're really fun to listen to and they write their own music!
), Regina Spektor (she is soooo talent), Shakira (yes, her sound is more "commercial", but she's soo experimental on her Spanish albums), Tori Amos and Wir sind Helden (they're awesomely catchy!).