repeating some of what was said above...
- yes, ride the (free) staten island ferry, the statue looks very nice from it
- ellis island is more interesting than the statue (i visited the statue once, when i was v. young. what i think i remember is that there was no guardrail around the perimeter. you could have walked right off the edge and fallen into the harbor. i'm assuming things have changed.)
- on the way back to manhattan, observe how the pollution follows the outline of the skyline
- dare i suggest ... while on staten island you can see minor league baseball a few minutes' walk from the ferry terminal (
http://web.minorleaguebaseball.com/index.jsp?sid=t586). inexpensive and you can get close to the field, but hokey. NB this is the lowest level of pro ball. if you want to see major league ball, don't even try to see the yankees, whose tickets are obscenely expensive and will be sold out anyway. see the mets, whose tickets are much less expensive and much more available.
- if you ride the 1 train (we call subways "trains") from the south ferry station (
http://en.wikipedia.org/wiki/Battery_Park) you can see behind glass (
http://www.ny1.com/content/news_beats/transit/90508/brand-new-south-ferry-station-to-open-soon/) a recently-discovered section of the 17th century sea wall which was much closer to the original shoreline (
http://www.nytimes.com/2006/03/01/nyregion/01wall.html)
- get a weekly metrocard, unlimited rides i believe (don't use it myself, but i think it's unlimited)
- most of manhattan is on a grid, it's made for walking, so plan a route and do alot of walking.