Wow, just looked at the map... Tenmile River is the next to last stop on the Harlem branch...
By train there are a couple of ways to get to Grand Central...
From JFK take the Airtrain to Jamaica
From Jamaica you have two choices...
1. take the E subway (short walk to the station) to 51st & Lexington and transfer to the 6 which will take to GC
2. Take LIRR to Woodside and transfer to the 7 train which will go to GC
3. Take LIRR to Penn Station... it is about a 15 minute walk to GC (not recommended if carrying a lot of bags)