So I don't know what your budget is when you say you're on a budget. It's incredibly difficult to recommend food, bars, or dancing places without a real dollar amount as you can go from $6 beers to $400 minimum bottle service and what counts as a "budget" for you isn't going to be the same as someone else.

There are lots of places with nice views but many are expensive. We even currently have a sticky thread about rooftop bars.

The place where the brokers do the trading is on Wall Street, but it's called the New York Stock Exchange. Unfortunately, they don't allow visitors the NYSE anymore, but there is the Museum of American Finance and the Federal Reserve Bank.

As for science and evolution, the American Museum of Natural History is tops. The New York Hall of Science might be a bit junior for you, but it is out in Flushing Meadows, which is a unique park that was once a Worlds Fair ground. It's also near The Queens Museum, which has a panorama of the city that is kinda cool.