If you travel to Eastbourne the best way to get around is by Eastbourne Buses. They are one of the few companies not controlled by Stagecoach.
They travel all around the town area with 4 different services serving the local hospital and inthe summer they run a popular "seafront service" which goes up to Beachy Head every hour. They are even trying to extend the Sunday and evening services in the town. The drivers are much friendlier than those on other services and their day trips to France are excellent value during the summer.
So, if you need to get in and around Eastbourne I would recommend Eastbourne Buses as the best mode of transport.