We always go to Kefalonia late May and the weather has been fantastic. yes a little cool in the evenings but who wants to sleep with air conditioning humming away? For those of you who want wonderful beaches, good (if plain) greek cooking , cheap wine and good beer and no "get your English breakfast here!" then this is the place for you. Yes some bars don't open till a few weeks later but then the beaches start getting crowded and the heat turns up. Went in mid September as well last year and enjoyed the benefit of warmer sea temps. However the wasps were a nuisance particularly in Fiskardo. May sees the Island at its best with wild flowers covering every available space!