10 days in London! Help!

Ritz, you could do a few nights in Paris, traveling from London via Eurostar.

https://www.eurostar.com/us-en/train/france/paris

With just 6 full sightseeing days to work with and never having never been to London, you might also just stay put? Make day trips (train) to Windsor/Eton, Hampton Court, Greenwich, etc. With some idea of your interests, the folks here can make some good suggestions. You can't really cram "a couple of other countries" + London (there is a lot to see just in and around the city!) into 6 days and do them any sort of justice, IMHO. That would also eat up too much time in transport. Paris is a good option for adding a 2nd location, though.

I would recommend just enjoying London and surrounding area since it is your first trip there. You could go to west coast of England or up north or to Edinburgh if you wanted -Edinburgh is just 4 hours by train or a quick flight. You could see quite a bit if you stayed 3 or 4 nights. Enjoy!

Completely agree with Kathy. Anything more than Paris and London would be too much, too quick. You wouldn't have time to enjoy it, let alone see much. I would choose Paris or Edinburgh for 2 nights, and the remainder in London if you definitely want to go to another country. When I went to Paris from London, train tickets were more than I wanted to pay and I ended up flying out of London City Airport for significantly cheaper. You might compare the two if you go with Paris.
Alternatively, don't rule out just staying in England and taking some day trips out of London. There is SO much to do and you won't get bored with it.

Kathy and others are right, "a couple of other countries while we are there" isn't a realistic plan. I suggest staying right in London, making a day trip or two if you want to Oxford, Cambridge, Canterbury, Hampton Court, Salisbury/Stonehenge, or any of the many interesting places near London, and sightseeing in the city. "Explore Europe" on this website has suggestions for varying amounts of time in and around London.

I wouldn't recommend adding a trip to Paris this week, though some people do. A one-day trip would be very rushed, and I don't see how you could get much enjoyment out of a city that is worth at least as much time as London, i.e. a week or more. An overnight trip would let you see more of Paris, but with time spent changing hotels. Save Paris, and those other countries, for another trip when you can give them the time and attention they deserve.

A one-day trip would be very rushed, and I don't see how you could get
much enjoyment out of a city that is worth at least as much time as
London, i.e. a week or more.

Just to clarify, I didn't recommend Paris for a one-day trip. I'd spend at least 3 nights or more unless there's not much about the City of Light which appeals. We spent a week there and had a hard time leaving! You don't have a week to spend but could get a feel for it over a few days.

I would do London and Scotland/slash/English countryside, just because London and Paris are both big cities and you may be "big-citied" out. Do NOT drive, trains are amazing and abundant everywhere and the mental energy it takes to drive on the other side of the road is just not worth it. Most international flights land at Heathrow, which has the quick Heathrow Express to take you into central London.

As far as hotels, if you tell us your budget and what kind of hotels you like (chains? local charm? American-style? need an elevator/lift [many English hotels don't have them]?) we can help advise you.

Finally, if you haven't read it already, get Rick's Great Britain guidebook - it's fantastic and very comprehensive. If you don't want to buy it most likely your library has it.

Ahhhh! Difficult to not go to Paris if you’ve never been. It’s my end all be all favorite! I would do half London and half Paris!

Kathy is the voice of reason. You cannot see another country: you can barely experience another city in the time you have. Best use of time and money is to stay in London, get an apartment. Since it is a long stay, and make a couple of day trips. Start a list of what you want to see and do in London and roughly figure out a day-by-day plan so you know how much time it will take before deciding on locations outside of London. When we go there we take one day trip per week to such paces as Canterbury or Windsor, Going to Paris or anywhere outside of England is expensive considering the time you have available,

hey ritz
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)
cross-pollinate.com
airbnb.com
aloha