There are no hotels in the beach area. The nearest hotels can be found in Rock Sound
town. Find hotels in Lighthouse
How to get there 
Fly to Nassau International Airport (NAS)
. Next fly to Eleuthera island to Governor's Harbour Airport (GHB)
(there are also some international flights to this airport). Next hire a taxi.
It is also possible to get to Eleuthera island by ferry. For example Bahamas Ferries
serves routes from capital Nassau island to Governor's Harbour
port of Eleuthera island. Find flights to Lighthouse
When to go 
During the dry season - from October to May. Also July is usually not too rainy.
Water temperature, C
Wind speed, meter/sec