Norm,

I agree with the others that recommend avoiding LGA. We fly in and out of JFK and stay at the Hilton Garden Inn (usually using a Park-n-Fly option), it is close, clean and has a very good shuttle service. We have used the shuttle as early as 5:00am and as late as 11:00pm with no problems.
If you do end up going to LGA and then on to JFK, I would recommend a car service. It is not as costly as a limo and a lot easier on the nerves than a taxi. That ride from LGA to JFK can sometimes be a bear. I wouldn't want to do it in the morning if I had a plane to catch, you never know how the traffic is going to be. I've taken 2 hours to get from the Holland Tunnel to JFK before. Good luck with whatever you do.
Phil