While the W. Hempstead line is fairly close to you ( I live 4 blocks from the house in question), you need to look at the LIRR schedule. This line is one of the worst. Rush hour trains are not too bad, only changing at Jamaica. But most off hour trains require an additional change at Valley Stream.
I know a number of people who drive from WH to the New Hyde Park station - a bit further but NHP is on the main line, plenty of express trains and you can park on the local streets.
Any other area questions, give me a call - I would be glad to help.
The Donnelly Group