MIT is one of the biggest researchers of AI and robotics.
A
Google Search on "MIT Robotics" shows that they have a ton of laboratories and groups associated with robotics. They have also graduated founders of many major robotics companies such as
iRobot the creators of the Roomba and many military robots.
MIT also is home to the famous
Kismet .
But as many have mentioned here, there are many colleges with good degrees in Computer Science (Artificial Intelligence), and Electrical/Mechanical Engineering. It really depends on what part of robotics interests you.
Another interesting career to pursue is animatronics or robots designed for the movies (though these days computer graphics seem to be taking over). But with more and more consumer "robots" popping up in the marketplace, it is likely that there is a good future in whatever types of robotics you get into.
Keep in mind that FIRST robots are just a tip of the iceberg. most other robots rely on a lot more AI than we use in autonmous, but as they say, FIRST is a microcosm of the real engineering world!