There are taxis from Eastbourne Station (and buses but infrequent and a quite long haul round the town).
About half of trains stop at Hampden Park on the way into Eastbourne (the others stop at HP on the way back out - the trains continue to Hastings). HP is a shorter taxi ride across to the ground, and there are taxis on the parade opposite the station - or canny travellers call one from the train 15 minutes ahead - 01323 726 726. No I don't have shares in them (though I do live round the corner.)
If you stay on the train until Westham, which is the next station after Hampden Park on the way to Hastings, you can actually walk to Priory Lane - it's a brisk but flat 15 minute walk, dead easy - come off the train, walk back across the level crossing and keep going. You actually see the majestic floodlight pylons rising from the atmospheric marshland as you walk...
Got all that ?
Happy travelling
Kevin Anderson
(BBC Southern Counties radio)