Depends on if you want to spend some time in the city or not. If you want to explore Manhattan, then yes staying in Manhattan would be best. If you just want convenience to JFK, stay at a Marriott nearby that has a shuttle. Just go to JFK and take the free shuttle
You can get from LGA to JFK airport by hired car, taxi, shuttle service, and train/bus combination. I usually just take the bus/metro combination, takes a little more than an hour to do and it's really easy and cheap.