I stayed for a week in Tingaki in May last year and would echo Robs comments on places to visit. I visited the saltpans at Tingaki most days and it produced some excellent birds such as Gull-billed Tern, Spur-winged Plover, Citrine Wag, Red-footed Falcon, Stone Curlew, Greater Flamingo as well as plenty of Little Stints, Black-winged Stilts, Squacco Herons, Kentish Povers etc. The water levels were already starting to drop though.
I saw a pr of Bonelli's Eagles at Old Pyli and found the top of the castle to be an ideal raptor viewpoint (also Blue Rock Thrush on top of the castle). The Old Pyli area also produced Short-toed Eagle, Long-legged Buzzard, Black-eared Wheatear, Eastern Subalpine Warbler & Cretzschmar's Bunting - also good for wild tortoises there!
Nissyros is said to be good for Orphean Warbler (though I didn't see these) but did have Audouin's Gull fly past whilst there, as well as Yelkouan & Cory's Shearwaters on the boat trip to and from the island.
Eleanora's Falcon & Lesser Kestrel are fairly widespread on Kos (though Nissyros had the largest concentration of Eleanora's). Keep checking telegraph wires when travelling around the island - that should eventually get you Roller.
Eastern Olivaceous Warblers are common & Black-headed Buntings were seen at the saltpans, on wires over the main street in Tingaki as well along various backroads inland of Tingaki.
Hope you have a memorable trip!
regards
Chris