Jeans are absolutely fine.
I personally prefer NY Waterways to the Circle Line, but they will both give you a nice view of The Statue of Liberty, UN, Ellis Island, Trade Ctr, etc. Just a few suggestions of things to do... obviously, you won't get to them all, but pick things you'd like to do depending on the weather and your interests. WALK WALK WALK!
Intrepid Air and Sea Museum, Trade Center, 9/11 Memeorial, Trinity Church (close by) and Wall Street. Rockefeller Center and St. Patrick's Church across the street. Grand Central, NY Public Library on 42nd St (amazing bldg) and the park in back, The Highline, Empire State Bldg, Chrysler Bldg, Flat Iron Bldg (you can sit in the street across from the Flat Iron and get a coffee at Eataly or cheese and nibbles at the park there), Washington Sq Park in the Village and all the side streets (McDougal, Bleeker ... ), Union Sq Market (check the days and times they are open), 5th & Madison Aves, all the amazing Museums, Lincoln Center (you're close). There is a booth in Times Square that sells last minute theater tickets for a fraction of the cost. Also, Chelsea, Chinatown and Soho are other wonderful areas in the city.
Just have fun. Walking is amzing, with so much to see. Do not eat at any chain restaurants!
Edited to add... THE YANKEES are home. Tickets to Yankee Stadium would be an amazing experience if you can get them. GO YANKEES!!!!