Getting to Brighton
You can get to Brighton on the Thameslink from anywhere in London pretty much. Its a quick train ride, and the services are frequent. Alternatively, you can get a train from Eastbourne and do the 7 sisters hike first like I did.
Seven Sisters
You can see the Seven sisters cliffs from Brighton, but it would take a rather long time to get there by foot. Id advise taking a train to Seaford first, hiking from Seaford to Eastbourne, and then taking a train from Eastbourne to Brighton.
The Seven Sisters are a beautiful set of cliffs in southern England, with rolling hills behind and a sheer drop to the ocean in front. Very nice, relatively easy day hike, totaling about 20km and minimal elevation.
Check out the Beachy Head lighthouse towards the end of the hike
Make sure you bring some sunscreen and water, and a decent windbreaker if you go when its chilly out.
Deceptively tropical looking water
Towards the end of the hike, the view into Eastbourne is also rather majestic. A welcome sight after a day of hiking around.
Brighton
Brighton itself is a rather charming beach town, though the beach is thoroughly unremarkable due to the pebbles. Its a decent place for a day trip solo, it could be more fun over a few days with some friends. Lots of overpriced entertainment on the strand, and some cool historical bits here and there as well. The pier is worth the 2 pounds to go see, and just wander about a bit.
The ruins of the old west promenade
Brighton Beach