Harrison Street is a restored historic block of elegant Federal townhouses which can give you a feel of the neighborhood in the 1700's. TriBeCa had been a center for textiles and dry goods throughout the 1800's; it wasn't until the 1960's that it really became a residential neighborhood as the warehouses moved to cheaper areas.
TriBeCa is also known for its film culture. The TriBeCa film center and its film festival add a lot of culture to the neighborhood.
Battery Park is located at the southern end of Manhattan. In 1623 the Dutch landed in what is now Manhattan, which they called New Amsterdam, and set up a fortification where the first "battery" of cannons would defend their new found land should they be attacked. They landed in what is now the lovely Battery Park. Their fortification still stands; it is called Castle Clinton after one of the early mayors of New York. It is now used as ticketing center for the ferries that run to the Statue of Liberty and Ellis Island.
Battery Park its self is a lovely area with open spaces to sit and enjoy the outdoors. The World Financial Center which borders the park provides a mall with many restaurants that look out onto the park. Farther toward the center of the island is Ground Zero, the World Trade Center site, which is now has a museum dedicated to the events of 9/11.
TriBeCa and Battery Park City offer 2 sorts of vacation rentals. There are high-rises in Battery Park that were built in the 1980 and later and in TriBeCa you can find older lofts. Vacation Rentals in this neighborhood tend to be expensive due to the exclusivity of the neighborhood.