Another vote for staying in Manhattan.
If you really don't want to go into Manhattan, though, I have very mixed feelings about staying at LGA vs. JFK. The one big advantage of staying at JFK is getting the ride out of the way so you don't have to worry about traffic getting to the airport. But I find JFK airport hotels incredibly depressing and the area offers almost nothing, while you can find cheap, top notch cuisine from every corner of the globe within a $10-15 Uber/Lyft ride from LGA (every kind of Chinese food imaginable in Flushing, Thai in Woodside, other East and Southeast Asian in Elmhurst, South Asian and Latin American in Jackson Heights, Greek and Middle Eastern in Astoria, etc.).