On the east coast, at Vathy, there’s a cave with a mixture of problems, above deep water. Usually you hire a local boat to get you there (about a kilometre down the inlet/’fjord’. More easy to get to is the opposite (south) side of the Vathy inlet where you can start from the swimming ‘pool’ at the harbour and traverse out for about half a kilometre. Mainly it’s easy scrambling interspersed with interesting 5+/6a+ sections (but you’re very close to the water) until the final section where you turn a steep corner and…. well, you’ll find out when you get there! Non-serious and great fun, with a nice cafe waiting to greet you on your return.
I gather there’s other deep water soloing venues on the west coast, near to the main climbing areas, near Kantouni and, less accessible, near North Cape. But I’ve not tried these… yet!
All-day climbing venues, old and new, are suitable for summer: Afternoon, Summertime and Local Freezer being quite close to Masouri. The new sector, ET, in the Vathy valley can be surprisingly cool on some summer days. To be quite honest though, most of the usual nearby crags can be climbed on ’til early afternoon as west is the predominent aspect.