hey hey ghackb
like others have mentioned, one city would be better with your time frame. it's your vacation though so it's your decision to go to paris. if you do both, book a multicity flight: atlanta to london/ paris to atlanta (no backtracking)
eurostar.com booking way ahead of time (couple months) is more budget friendly. keep an eye on it.
so much to see and do in london, have your kids get involved, have them plan one day each what they want. it's a compromise if someone not that into it.
discoverwalks.com/ london
withlocals.com/ london
getyourguide.com
many different things to do and see
be prepared if wanting to see changing of the guard at palace. checkdate/times (rct.uk/ visit). lots of people, very crowded, if short hard to see with many in front of you, long wait time when you get there early, wear comfy shoes, have cameras ready. it's a sight to see, we loved it. saw the horses galloping down the road in perfect harmony, also at the wellington barracks on birdcage walk is where the guard and band form.
wowcher.uk.co
register with email (free), it's like groupon. under more click what you want to look at. some are 2 for 1 price, afternoon tea, theatre tickets, river boat rides, dining/restaurants, etc
walks.com
look at all the different walks available and what days/times
streetsensation.co.uk/ markets
list of street markets, where, times, what they offer as in goods, food,
stmartin-in-the-fields.org
historic building and church, have lunch in cafe
freetoursbyfoot.com
many different tours/activities to see and do. you will not see everything. make a list of must do's, okay to miss, no time. have a map of london and mark where places are and combine them to what you plan to see in that area that day.
b-bakery.com
afternoon tea, chose which tour you want) on the big red double decker bus. takes you past known attractions in the city while having goodies on board to enjoy.
sixinthecity.co.uk/ walks
visitbrighton.com
a day trip by train away from london to have fun at the beach/boardwalk
thamesrockets.com
speedboat rides down the thames river
londonboxoffice.co.uk
cheap theatre tickets if interested
jasons.co.uk
boat ride down the regent's canal from little venice to camden lock
aladyinlondon.com
scroll down to search put in brighton beach with ideas there
or look at other places, days trips from london in popular posts, all your gang would enjoy
my novel is done, gives you lots to look at, think about, do your research along with the kids. have fun and enjoy
aloha