You don’t say where you are coming from.
Brighton's nearest airport is of course Shoreham. Its open until 20-00 local. Don’t even try and land or depart after! The VRP to the East is Brighton marina from which tracking inbound you will have a good view of Brighton city. Shoreham is friendly and worth a stop for a coffee if you like. Alternatives in the area are Goodwood (but closes at 18-00 to non locals) and further East Headcorn. Headcorn is great as they don’t close until sunset, very friendly and a cheap landing fee (free if you want fuel). Watch out for parachuting.
Have a good one!
PS the coast along to the Seven sisters and Eastbourne is very pretty (to the East of Brighton) and depending where you are coming form maybe up to Headcorn and then around the Gatwick zone.