like others have stated here, stay in london. lots to do and see without cramming. you say you're arriving saturday before first game on sunday, and may be jetlagged, something to think about, since i gather you're coming from USA. have you booked your flights already? check your arrival and departure times (too early to check in and do they have baggage storage and being at the airport at 6am for flight back)
renting an apartment is the way to go with you guys being there that long, more space to move around in, kithcen, living space, some have washers, pack light!, terrace. look where you want to stay, close to transportation, things to do. book early when you decide your dates, london is a busy crowded city and fun place. couple years ago we were there at the time oakland raiders played, regent street was crazy, decorated with NFL banners, red white & blue flags everywhere, crowded streets, happy tourists and football fans, a site to see for us. walk around, shops, restaurants, cafes, "free" entertainment. you'll be in awe and have a fabulous time.
do your research, buy tickets you need ahead of time, have a map and mark what you what to see, go to, and do. few "londoners/englanders" on this forum will be happy to help you with the good bad and ugly. once you decide on things come back and ask questions. no car needed
booking.com (put filters in on left side)