North Terminal.
South
They don't currently fly from Gatwick.
South Terminal.
South Terminal.
North Terminal.
South Terminal.
North Terminal.
North terminal
Thomson Airways fly from Terminal 2 to Alicante.
Easyjet and British Airways both fly to Nice from the North Terminal Monarch fly to Nice from the South Terminal.
British Airways fly to Barbados from North Terminal.
You may not have the choice, only certain airlines fly in to Gatwick.
Eastbourne doesn't have an airport - the nearest is Gatwick, so you would have to fly from Edinburgh to Gatwick and take a train from Gatwick to Eastbourne.