People often ask about running electronics off a dynamo hub, and you'd be surprised how complicated and expensive it is. Basically it's not worth even trying unless you are going to be riding away from a power outlet for several days at a time. Dynamo hubs put out AC with a widely varying voltage, often going down to zero (obviously). A system that converts that to a relatively constant DC supply is not trivial and requires a battery. I've done the easier thing and mounted a USB battery pack to my bike. A $20 battery can keep my phone running with the screen on all day. I charge my battery once a day, though I could get away with doing it every three or four days. Charging once a day is better for me because it's an easier habit to keep.

My favorite battery is the Anker Astro E1. It has proven to be reliable and durable.