iPhone 5 battery problem.

I just ponied up over $600 for a new black iPhone 5, 16 gig and I'm having the exact problem. Not very impressed AT ALL.

The brightness is low.

I've turned off almost all push notifications.

4g off / only using wifi.

Etc. etc. etc, bottom line = I don't use it very much and it's down 25% every half an hour.

Left it at 98% last night and woke up to a generous 1% this morning, that being the final straw.

I bought my iPhone in Miami, USA. I'm in Geneva, Switzerland right now. If I go to the local apple store will they be able to replace it for me? I'm not worried about the warranty as I just bought it several weeks ago but will the region difference matter?

I love iPhone but this is just unacceptable, how can I recommend and tout this to my friends as the champion of phones when it's causing me such stress?

Help.

-HJF