New York in 2098
Short: Same as now.
Similar to the early 21st century New York is a Juxtaposition of new and old. Buildings hundreds of years old stand next to some of the tallest skyscrapers. Its still the center of commerce for the US and still a bustling, thriving, dirty, amazing city. The poor and rich live together. The rich living in the nearly brand new high rises, and the poor living in the decades maybe centuries old buildings right next door. One thing that has changed dramatically over the years is the transit systems. Most of the populace, rich or poor, take public transit, leaving the streets for the tourists. This has alleviated much of the traffic issues, but a jam around rush hour is not unheard of. If you have a family you probably live in the suburbs. You can afford it on your FBI salary, otherwise you probably live in an apartment of some sort in-town.
As FBI agents you know that violent crime in NY City has not been reduced by gun control laws enacted in the past decades, but it has helped. As a FBI agent your are not as limited by standard gun control laws, but it is illegal to have unregistered or illegal weapons.
You are one of over 2000 agents at the New York Office. It is currently the 3rd largest office in the US and as rising stars (if the shoe fits) you have a quite prestigious position.