Skip the battery: I have a Supernova dynamo hub for my front wheel. From it I'm able to charge GPS or cellphone while riding, though it takes minimum 4 mph for the Garmin 705, 8 mph for an iPhone 5. The hub uses 1-2 watts to turn it, almost nothing. Power is regulated by one of these:
http://www.sinewavecycles.com/products/sinewave-revolution . The hub and power converter are both waterproof. A little searching can find dynamo hubs for through-axles, snow bikes, whatever.
I tried a Goal 0 solar panel, it used two small solar panels to charge 4 AA batteries or what ever you plugged into it. I did okay with just a GPS but could do nothing for a phone. The battery pack they sell (separately) can be charged from a 120 v outlet, so maybe that is what you are looking for.
http://www.goalzero.com/p/133/guide-10-plus-recharger
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