Actually, the correct answer is that no one is buried at Grant's Tomb, rather Grant and his wife Julia are either "interred" or "entombed" there.
The NYC insider (at
http://www.theinsider.com/nyc/attractions/2general.htm) explains it like this:
Who's Buried in Grant's Tomb?
This is an old joke to which the answer is no one. Our eighteenth president and his wife are, however, entombed here. Made of 8,000 tons of granite, with Massachusetts marble for the floors and fine Italian marble for the railings and trimmings, Grant's Tomb sits high above the Hudson River in the midst of a beautiful park. It was once one of the most popular attractions in New York City, although it rarely attracts much of a crowd today.
The History of Grant's Tomb
Ulysses Simpson Grant, a Civil War hero who was thought to be chiefly responsible for the defeat of the Confederacy, was perhaps the most popular American in his day. Although his eight-year presidency was marred by government corruption, Grant was nevertheless held in great esteem by millions of Americans when he died (of throat cancer) on July 23, 1885.
Even before his death, the Grant Monument Association had been formed to raise funds for constructing a monument in his name. Ultimately, 90,000 people donated $600,000 to the project. At the time, this was the most money that had ever been raised for a public monument. Given Grant's popularity, it was a major coup for New York City when William Grace, the city's mayor, secured the site where the monument now stands as Grant's final resting place. There is no doubt, however, that this political victory was aided by Grant's request that he be buried in St. Louis, Galena, Illinois, or New York City, rather than Washington D.C.
more at the link.