If I had to choose between the two then I would stay at the George. Livin Mykonos is not in a very convenient location whereas at the George platis yialos beach is just a short walk away and you have a regular and reliable bus service into town which in August will run until the early hours of the morning
I wouldn't stay in town. Try Maganos Frangiska Apartment. I stayed there last year and am going again this year. Room rate includes home cooked breakfast and lunch by the lovely Anna. Amazing. Near 2 bars and the beach and also short walk to the bus into town.
I don't know those hotels, but definitely stay in the beach area! The town is all shops and there is no real beach nearby and it will be very hot! The beach has a nice breeze and restaurants and you can take the bus into town for nightlife if you want!