I'd say Rye, Cuckmere and Pevensey Levels are your best bets. Seaford Head and Beachy Head are generally quiet in Mid-may, but their is a chance of Wood Warbler, Pied Flycatcher or even an overshooting med species e.g Golden Oriole or Bee-eater, but main migration has gone. Rye and the Cuckmere are good for migrating waders, but I'd say Pett Level Pools are definitely worth a stop, you might well see Spotshank, Wood Sand, Yellow Wagtail and plenty of others good birds. Rye is fairly well documented for what you will see, but Pevensey also has a fairly good chance of waders, and also quite possibly GW Egret and Purple Heron. There are sometimes small concentrations of Hobbies hawking over it, and a few Yellow Wags and Tree Sparrows breed. If you want to visit the south downs, there is a nice secluded spot near me called Greenway Bottom which in Mid-may will most likely have Turtle Dove, Hobby, five species of warbler and possibly Quail. also Abbot's Wood is a great spot for Nightingales, Turtle Doves and Garden Warblers, and Ashdown Forest was Crossbill, Redstart, Nightjar, Woodcock etc. with the best area being Old Lodge
sorry for the rant I just get very passionate about my home county sometimes!!
Hope I helped and you have a great stay down here!