Since I'm there everyday, I'm probably the last person that should be giving you recommendations on what to see in the city. There are about a million museums, restaurants, parks, 2 brand spankin new MLB stadiums, the old World Trade Center site, Statue of liberty, more skyscrapers than you can imagine not to mention tons of people that will try to scam the tourists. That being said, I think the best thing you can do is walk Manhattan. Start at the "Bull" on Broadway just south of Wall St. and walk north to Times Square. Walk east on one of the streets in in the upper 40's, theater district, until you get to either 5th Ave or Park Ave then walk north again for about 10 or so more blocks. This will probably take you about 4-5 hours but you will see more about the city than you would if you had an agenda. Along the way I'm sure you will be stopping at the Empire State Bldg, Rock Center, Wall St, Ground Zero, Canal St, Radio City, etc.... There is way to much to do in 3 days.
For the Boardwalk, head to the Jersey Shore. Point Pleasant, Seaside Heights (MTV fame), Atlantic City, Wildwood, CapeMay all have boardwalks with rides, stands, and beautiful wide beaches.
Hope that gives you some ideas.
Joe