WHere to find new Casters?  

Glides
What you are looking for are called glides. I believe the Eiffel base has 2 possible configurations for glides either the snap on or "domes of silence" You can find them on ebay sometimes but there are plenty of reproductions available at sites like Hume Modern. You can also try and contact Herman Miller directly. Either way expect a set of 4 glides to cost around 20 bucks.
Good Luck!

Glides
One would be referred to as a plastic glide. At least that's what we used to call them when I represented a few furniture lines back in the early eighties.

thank you
thank you that is the name I'm looking for. The glides are for a generic base so I'm going to have to look and see how they were put on and if I can get the broken ones out to measure the base. Thank you again!

Glides
Typical glides for Herman Miller's eiffel tower base simply snap on, assuming you don't have the "dome of silence" ones. I've placed them on authentic Herman Miller bases as well as reproductions. I got em on Ebay from the same buyer a few times.
Dome of Silence is the first image
The second is the snap on.
Good luck

Hume Glides and Removing broken Glides
I actually had to order a set of 4 glides for an Aluminum Group chair a few months ago. They did not have the original white glides but fortunately the black ones looked just as well as the chair is in black leather. Total with shipping was right at $40. Have to say they were well worth it and Hume was great to deal with.
Tip for getting the old plastic out of the base. With a 1/8 bit, drill a hole in the center of the old plastic glide. Helps if the remaining part of the glide is smoothed over or flush. Then screw in a 2" or longer wood or sheet metal screw that is a tad wider than the 1/8 hole. Leave at least an inch of the screw showing. Pull out old glide with a pair of pliers by gripping screw. Whole process is somewhat like using a cork screw on a bottle of vino.
Good luck.

Glides
Replacement snap-on nylon glides are commonly available on eBay. They will fit the vintage Eiffel tower base.
The current Vitra base uses a slightly different size. I would suggest contacting Herman Miller or Vitra for replacements of that kind.