The opinions expressed on this page are my own and do not represent the policy or opinions of the economics department. The recommendations here are based primarily on the success of students who have taken the path I describe.
Math is the language of economics. If you are an NYU undergraduate, studying math will open doors to you in terms of interesting economics courses at NYU and job opportunities afterwards. Start with the basics: take three calculus courses (up to and including multivariable calculus), linear algebra, and a good course in probability and statistics. These basic courses will empower you. After you have these under your belt, you have many interesting options all of which will further empower you to learn and practice economics. I especially recommend courses in (1) Markov chains and stochastic processes, and (2) differential equations.
Superb economists at NYU (e.g., Robert Engle, Xavier Gabaix, Stanley Zin, Jess Benhabib, Douglas Gale, Boyan Jovanovic, David Pearce, Debraj Ray, Ennio Stacchetti, Charles Wilson, and others) have made notable contributions to economics partly because they are very creative but also because they studied more math than others.
My personal opinion is that if you are an undergraduate at Stern or the NYU CAS economics department and you are seriously interested in learning as much rigorous economics as you can at NYU, you will be much better off taking one or two additional math and statistics courses rather than spending time and credits writing an undergraduate honors thesis. This will also look better on your transcript if you plan to apply to graduate school.
These courses listed above are very useful courses for applied work in econometrics, macroeconomic theory, and applied industrial organization. They describe the foundations of methods used to specify and estimate dynamic competitive models.
Just as in jogging, I recommend not overdoing it. Rather, find a pace that you can sustain throughout your years here. You will find that taking these courses doesn't really cost time, because of your improved efficiency in doing economics.
There are many other courses that are interesting and useful. The most important thing is just to get started acquiring the tools and habits these courses will convey.