If your budget is $250, wait a couple of more weeks for the iPhone 5 to come out, then pick up a gently used iPhone 4 (not 3G or 3GS) on Craigslist. Should be maybe $250 by then. Then pick up a Mophie Juice pack
for about $50, and your battery problem is mostly solved.
While Android is getting a lot of activations and their App Store is getting better every day, Apple's App Store has far and away better quality apps. You can turn your iPhone into a backcountry GPS, hook it up to Spot puck, etc.