Lots of Paris info posted already so I'll give you some tips on London.

- Late June and early July are great times. There's Wimbledon going on, not too cold or too hot.

- West End (Theater district) is my favorite place to stay. In the middle of the action with some great pubs and people watching. Walking distance British Museum, National Gallery. Plenty of tube stations in the area.

- Use AirBNB!!! Found a great London flat for 7 nights last October that was 2 blocks from a major tube station, in a prime area, well furnished with a full kitchen. Much better value than the hotel options, especially if it's more than 2 people in your group.

- I just read about LaCompagnie flights. It business-class only flights from NY to both London and Paris and only about $1600 round trip. Will have to fly different airline to connect to NY, but no biggie.

- If considering day trip to surrounding area (Bath, Dover cliffs, Canterbury) then I would steer clear of the big bus tour packages. Not fun to be packed in a bus with 40 other tourists, most of which are loud and obnoxious from Ohio or Minnesota. If you don't notice any annoying tourists, then it's YOU! I would take a train to Bath and would take a small group tour (by van) to other sites. Wouldn't bother with Stonehenge - you can't walk up and touch them anymore and it's a long ride.

- London is about taking in history, architecture, people watching and stopping for beer several times in between. The open-top bus tours are overwhelming - you quickly lose your sense of direction and fly by sights without the opportunity to pause and take pics. Instead I would do historical walking tours focusing on one or two districts per day. There are smartphone apps that will guide you around an area and once triggered by gps will tell you what you are looking at. Very cool!