From the looks of things, you never got clear answers to any of your questions. And never ask a hater from Boston for his opinions about anything (e.g. where to fly into, how to correctly pronounce "chowder," sensible tax policy, etc.)
You should fly into: La Guardia (JFK is a nightmare and if it's your first time here you don't want to deal with Newark and getting into NYC from NJ). Once you arrive at LGA, your only option for getting into the city will be cab, unless you are staying in a hotel with one of those little buses that will pick you up at the airport. When leaving LGA, you can choose between a regular taxi or one of these annoying "black cars" (no, I don't mean an Escalade with gold trim, but rather a Lincoln Town Car that costs a bit more than a regular cab). Just go with the cab because you usually end up sharing the town car with someone you don't know.
Where you should stay: You should absolutely stay in MANHATTAN -- preferably midtown. Staying anywhere else defeats the purpose of coming to NYC. You sure as hell didn't come to see Northern NJ or one of the outer burros. Per specific hotel recommendations, it all depends on what you want to spend. A firm I was doing work for put me up at this place for a week and the rooms were nice enough given the rates.
http://www.kimberlyhotel.com/
At a minimum you'll be looking at $400/per night.
What to See, Where to Shop, Dine, Etc: Of course you'll hit the obvious landmarks, maybe add to your list The Cloisters, Whitney Museum, Museum of Modern Art, Central Park Zoo, Top of Rockefeller Center, Rainbow Room (also at Rockefeller Center - jacket & tie may be required), Little Italy, Chinatown, NYSE, check online for shows currently on Broadway and maybe see about a matinee. Your high-end shopping is on 5th Ave in the upper 40's/lower 50's. Per trendy places to eat, you'll have to look elsewhere. Tavern on the Green is an iconic New York restaurant though on Central Park.
See
http://nycvisit.com/ for more info.