It is what it sounds like, very commercial, dead on the weekends crowded on weekdays, mostly restaurants that cater to office workers.
Keep google maps handy, financial district is kind of twisty and turny not the easy grid of streets you'll find to the north.
You've got big crowds near World Trade, Battery Park is really nice, you're near the ferries to the Statue of Liberty, Staten Island, and Governer's Island. The entrance to the Brooklyn Bridge is also down there and there's a nice view at South st seaport. If you wan't good food you'll mostly be going elsewhere but you'll have fairly easy access to the A, C, E, N, R and 4,5, 6 trains. Also note, if you want to actually ENTER the statue of liberty you have to make an appointment well in advance, like, look into it now and see how far in advance you need to book it. If seeing it is good enough you can opt to take the Staten Island ferry which is free and just gawk at it as you pass by and then take the ferry right back.
One thing I've noticed is that visitors are often not prepared to do a lot of walking. Bring some comfortable shoes.
I'd say take the subway more than taxi or uber, there's a whole world of sights, smells and panhandling you're gonna miss otherwise.
Opt for Rockefeller Center instead of Empire State building if you want to hit a skyscraper.
