There is a lot of family activities to do in London. I have been there about 20 times myself and it is easily in in the top 5 of my most favorite cities. Lots of culture and historical experiences to be had here. For a short time like you have, look into doing one of the All Day tours that you book from the hotel. Winsdor/Bath/Stone Henge is one that is relatively cheap and a good way to see a lot of the outlying areas of London as well. The tour guides are very well informed and you will be surprised to learn some of the things you may not know. (In terms of acreage and space - parks and such - London is the greenest city of its size.)
Or you can book a Hop On Hop Off bus and scoot around town to different areas of your choice on the map that reflect your interests.
I was there this past May and while London is notorious for having wet/bad weather, it was absolutely beautiful then. It was actually so warm that the Chelsea Flower Show was in a tizzy because the warm weather was causing everything to bloom ahead of schedule and the festival was still a bit away. There is plenty to do, so just enjoy it and have fun.
The food is great there. Well, all the food except British food. They are the blandest cooks of all time apparently. But you can find some fantastic American, Paki, Chinese, etc... places to eat.
Paris is not that bad either. I was there again at the first of December last year and it is still a beautiful city even in cold weather. Yeah, there are "areas" that are gritty and where you don't want to go, but overall the city is terrific and worth a few visits to over the years.
