you should look at a tourist map first and try to group things. Battery Park is nothing special.

First - rethink a bike in Central Park. Bikes are allowed only on the roads - not the pedestrian paths - and you can't really see very much from them. The other thing is that the bikers tend to be going fairly fast - for exercise - and I doubt an 8 year old could keep up. If he is riding by himself on a small kids bike he could - carefully - ride on the pedestrian paths - but you would have to walk - or trot - along.

As for the other sights - you need a good street map of the city with the sights indicated as well as a good subway map. That will help you group things.

Agree Battery Park City doesn;t have much to see/do - just a residential complex on the lower hudson.

And if you want to do shows you should get tickets as soon as you have your dates - to make sure you have the best choice of seats (and I've never seen Lion King discount).

Check to see if the Staten Island Yankees are in town. My daughter and I went when she was about the same age and had a great time. The stadium is right where the ferry lets you out on Staten Island and has a view back over to Manhattan. The game was a ton of fun and waaay cheaper and easier than an actual Yankees game.

But....the real Yankees game that we went to a few years later was also an experience.

My at-the-time 7- and 8.5-year-old nephews enjoyed a few hours exploring the parks along the river north of Battery Park, in particular the Nelson A. Rockefeller Park. this park is very family friendly with lawns, fish pond, a great playground, ping pong and Nok hockey games and the Otterness sculpture installation at its north end. Nearby Teardrop Park was also a hit with its forest-like pathways and two-storey slide. Just north of Rockefeller Park, Pier 25 has a miniature golf course.