Where should we stay to catch a British Airways flight out of Gatwick at 1030 am?

Gatwick Express is every 15 mins from 5am and takes half an hour. Stay near Victoria Station. .

Take the Gatwick express so you arrive at least 3 hours before the flight if you have to check in;
or 2 hours if you checked in online got a boarding pass and need to just go through security.

The Corner House Hotel, Horley.....5 minutes from Gatwick and they provide transportation to the airport.

Luna & Simone near Victoria Station is very nice and a double/twin goes for £128 per night.

Take a train down to Gatwick to avoid the real possibility, particularly in the morning rush hour, of sitting immobilized in stopped traffic as your flight leaves.

BA will have fixed times prior to departure after which you can't check bags or check in. Check around their site.

Thank you. I will check out the suggested hotels and Thameslink for the other nights and timing. Someone on TripAdvisor suggested a chain called Premier also nearer Gatwick. Anyone have opinions on that?

Premier Inn was a good deal when we stayed there, but a bit strange. Very comfy beds and pillows, quiet and safe, but almost everything else was an extra charge, so just watch your details if you go with them (wifi, soap, etc). If you stay at Sidney Hotel near Victoria Station, that will make the bus trip to the Harry Potter Studios trip super easy. Their prices (and legit reviews) were good, the last that I looked.
My personal preference when I go to London is to stay as very close to where I want to be, and just pay extra to be able to avoid yet more travel and complications. Travelodges have been good, basic but comfy, and good hot breakfasts for low prices. I have found they are not on many other travel sites, sometimes not even on Google maps, so you have to go on the travelodge.co.uk web site to find them, but usually worth it. :) That's the sneaky back door tip I figured out on my last trip (excellent for Windsor, once you know to arrive on the Riverside train station, not the other one, so you can find their entry door that's up over a huge parking garage, long story). Good luck!

One of the advantages to staying at Gatwick airport the night before, which we do, is the facility to check your hold luggage the evening before. BA evening check in is available for flights leaving before 15.15 the next day and is open until 22.00 so no need to spend too much time at the airport. We have a change of clothes and minimum toiletries in our hand luggage and go straight to Security the following morning.

http://www.gatwickairport.com/at-the-airport/flying-out/check-in/day-before-check-in/

There are a number of on-airport hotels to chose from. The shuttle link between the North and South terminals is frequent and only takes a matter of minutes so the location of the hotel is not important

http://www.gatwickairport.com/at-the-airport/passenger-services/airport-hotels/