Allow me to weigh in as a frequent NYC visitor who has used all three airports.
If you're flying coach to NYC, and you're into public transportation, and you're staying at the Marriott Marquis, I'd say EWR and take the train as described above. It would be the least prone to rush hour delays of all your ground transportation options.
If you're upgrading your flight, and comfort level while flying is of importance (which it is to me), I'd take one of the BusinessElite flights into JFK (which means you'd have to connect in ATL) and then grab a taxi from there for $35 plus tolls and tips.
If you're definitely flying coach and you don't like public transportation, I'd say LGA. It's the shortest taxi ride -- although the more west you stay in Manhattan, the longer it takes and the less advantageous it becomes compared to EWR.
You didn't ask, but if it were me I would use my Marriott points and stay at the Marriott East Side on Lexington Avenue rather than the Marriott Marquis. From the east side, you are really close to LGA (roughly $18-20 by taxi, 20 minutes except during rush hour). Unless your whole goal is to walk around Times Square, I think the east side location is generally better.
Finally, regarding restaurants: given that NYC is one of the world's great restaurant cities, that's a hard question to answer not knowing what you like. Several places where you can't miss include:
1. Gotham Bar and Grill (still packing them in after 15 years or so with a nice new American menu; try the New York Strip with Vidalia Onion Rings)
2. Manhattan Ocean Club (get the Dover Sole, but it often runs out so you might call and have them hold one for you)
3. Grammercy Tavern
4. Oceana (if you want really delicioius, expensive, high end seafood; jacket required)
5. Scalinatella (a little downstairs Italian place with good food, and as a bonus it's open for lunch on Saturday).
There are hundreds of other restaurants that someone else could easily make an argument for. I'd suggest a visit to Zagat.com.
Enjoy NYC.