Well, the Arsenal Emirates Stadium is in Holloway, North East London, nearest tube station Arsenal, on the Piccadilly line, whereas Fulham is in South West London, nearest stations Fulham Broadway or Putney Bridge.
The Round House is in Camden - nearest tube Chalk Farm, on the Northern Line, Edgware Branch. So it depends how adventurous you want to be in terms of travel in the City
With regard to hotels, I would really need more of an idea of what your budget per night would be before I can advise you. London is now, sadly, close to the most expensive city in the world to visit. Prices start at around £10 a night for a reasonable hostel to... well, the sky's the limit really.
PM me if I can give you any more help.
J x