You might want to listen to bands like Bell X1, Keane, Radiohead, South, Snow Patrol, Oasis, Suede, Travis, Placebo, Doves, Blur, and World Leader Pretend. You can also use Pandora.com to find alternative songs or bands similar to Coldplay.
Alternative is a huge category. Check out some of the older bands, too. Like BeBop Deluxe and Shriekback. Camper Van Beethoven are tasty. If you feel adventurous, try Wire, Fugazi, or Sonic Youth. To get really freaky, play some Captain Beefheart or Pere Ubu. Lot of excellent women doing Alternative too: The Breeders, the Raincoats, L7, Laurie Anderson, Cat Power... Okay, I'll stop now.