London Airports

you don't say you're staying in London so let's assume you're not

in that case taking the national express coach direct from Heathrow to Gatwick would be easiest (allow several hours then add 20%)

Are you staying in London first or are you trying to connect on the same day that your transatlantic flight arrives?

If the former, where are you staying in London? Generally, I would choose Gatwick for Easyjet if the time were convenient.

If the latter, I'd recommend you see if it is possible to fly BA out of LHR.

Your problem maybe that you are buying separate tickets, rather than being ticketed through to Nice, so if your incoming flight is delayed by a couple of hours, then you may miss your onward flight to Nice and the cost of a replacement ticket will be down to yourself, not the airline. So you need to allow a good margin of time for delays.

Why do you think London City is a better option? It's on the opposite side of London. There is only 1 direct flight a day from London City to Nice at the weekend and 2 during the midweek, so this isn't that good an option, as you risk being stuck there overnight. There are direct flights from Heathrow to Nice on BA, which maybe easier than transferring to Gatwick.

Heathrow to Gatwick - there are regular buses that take between 50 and 75 minutes, depending on which terminal you are using at each end. They run every 30 minutes or so off peak and between 3 and 5 buses per hour at other times. Allow at least an hour for your plane to land and to get through immigration - having only hand luggage will only save you 5 minutes. Another 15 minutes to find the coach stop. You may have to wait for up to 30 minutes for the coach, so that's 4 hours from landing to reaching Gatwick if all goes well. You will need to be at Gatwick a minimum of 75 minutes before your flight to get through baggage checks etc.

Your unknown margin is what to allow for delays to your incoming flight plus travel problems on the road. Unless you can afford to buy another ticket on the day if you miss your connection, out of Gatwick, I would be looking for a departure at least 6 hours after landing at Heathrow. In addition, most of the Easyjet flights I have taken recently have been full, so there may not be an option to book a later flight on the same day if you were to miss it. Plus this will be expensive.

Far less stress if you fly out of Heathrow, particularly with a 7 year old. An even better option would be to change your ticket to book through to Nice, if possible then the risk is with the airline.

Jennifer offers very good advice. If you are flying trans-Atlantic, getting a ticket that connects to Nice will be far less stressful. It doesn't matter which airport you are using for easyJet (and other no-frills airlines) you will have to go through all the time-consuming intricacies of entering the UK (because it is not part of the Schengen area), claiming your luggage, checking back in with easyJet (which you should do far in advance on-line). That airline has far stricter luggage rules. Then you will do the entry procedures, customs etc. again in Nice. Should your first flight come in too late to make the easyJet departure, that ticket will be completely forfeit. Plus I doubt you will save much money doing it yourself, as the long-range airlines have been forced to compete with the budget carriers on these short hops in Europe.

this is all very helpful! Thank you! We already have tickets from Chicago to London - very cheap day flight. So we will sleep at heathrow and then make our way to Nice. The flights from heathrow are a lot more expensive but I need to figure it out with the time and the cost to get to Gatwick. On our return from Nice we will have 3 nights in London before returning to the US. I booked a hotel in Shoreditch. If I end up buying one ways would it be easier to fly Nice - London City on that leg of the trip?

Where in Shoreditch? Since it is a hipster neighborhood now (much different than when my ancestors lived there 150 years ago) a lot of nearby neighborhoods borrow the name even if they are fairly far away.

If it works out right you may be able to get quite close using TfL Overground. Or not. All depends on where.

would it be easier to fly Nice - London City on that leg of the trip?

It might be but it's really not worth over thinking this. Public transport and/or taxis will get you everywhere you want go.