If you are a Harry Potter fan, you'll love the tour. If not, you'll think it is a total rip. It will be crowded as Hell. Bring snacks unless you enjoy paying top dollar for food. Book early and if you get a late tour, show up a couple hours early, they will probably let you in any way.
I didn't do the Eye or go on the Eiffel Tower. The lines are nuts and a poor use of time. Climb to the top of St. Paul's Cathedral (check out the ancient graffiti along the way) for a great view of London. If you bring some nice clothes (dress code), London Sky Garden is free before 10 and that is an even better view, plus they have elevators. Notre-Dame and Arc de Triomphe provide great views of Paris.
London - Do a bus tour early to get a feel for where everything is. I really enjoyed the museums and cathedrals. Churchhill's War Rooms was a bust for us. Shakespeare's Globe Theatre tour was very cool, but mostly because of the Cockney tour guide. The parks are amazing. We really liked Kew Gardens. Eat a hearty English breakfast at a local place for ~5 pounds. You are going to do a lot of walking. Wear good shoes and fresh socks.
Paris - If you are taking the Eurostar from London, be prepared, the area around Gare du Norde is sketchy AF. We survived though. If you don't speak French, try to learn the polite words. Most of them speak English and if you just try, they will help you out. Amazing museums. Check out the Catacombs (early in the day) for something different. The French are not big on breakfast, so we'd grab some bread the day prior. Fancy bread is dirt cheap there. Beer is cheaper than Coke. Again, lot's of walking.
We did a week in both London and Paris last year. London rents are expensive. Paris is actually somewhat cheap. Get copies of Rick Steves' guides to both cities. They really come in handy. We used Airbnb.
Who's your cell provider? If T-Mobile, your gonna love it. Just confirm before you leave, international service isn't blocked on any of your lines. I had one line that was blocked for some reason and it was a pain in the ass.