There are a few camping sites and caravan parks dotted around the Brighton & Hove area - we've tried to put together a thorough list below. If you want a view of all the hotels available and their facilities, you can find our full listings here (you can filter by location there too!).
There are a few options for camping or driving a caravan down to the city - a couple of which are just on the edge and easy to grab a bus into town.
Starting with the two most central, we've got a Caravan Club site just at the eastern edge of the city near East Brighton Park which is only 5 minutes from a bus stop that'll take you into the centre. You can check their website here. Just a bit further out, there is a weekend pop-up campsite, over in Woodingdean, set up on the hills of the downs. You can bring your own tent or hire one of their larger bell tents and there are options to join in various activities, including morning yoga on the downs and whittling your own spoon! The site is only about 7 minutes drive from the centre - you can check the details out here.
Out of the city, between Brighton and Lewes and still in the south downs, is Housedean Farm Campsite. It's a fully equipped tent pitching campsite, with loos and showers, as well as a washing up shelter with a communal fridge/freezer. They allow small campervans (VW style) on site but have no connection points and don't accept larger caravans or mobile homes. It's ideally situated for a walk straight into the hills and is located on the South Downs Way - 20 miles from Eastbourne, if you're feeling very active! Apparently you can spot the Isle of Wight from the top of some hills on a very clear day! They also have a website, here.
Beyond those above, there is a great list of pitches and caravan spots available here, with some as close as Lancing (which is only 15 minutes by train), or 7 miles or so in a straight line.