Chad,
I don't know a whole lot about the specs of the equipment or antennas the FAA uses, but I can tell you that the antennas are located all over the place, often on remote mountain tops. Just a wild guess, but I would bet that each center has around 10-15 antenna locations at minimum. The actual physical location for Denver Center is in Longmont. From there, the transmissions are relayed through various means (microwave, landline, etc) to and from the remote locations. Same goes for the radar feeds. There are radars in remote locations to ensure complete coverage over the center's area of responsibility.
I was considering trying to get a group together to see about touring either TRACON out at DIA (which I've been to twice), or the ARTCC in Longmont (which I have not been to). Just got to get this training out of the way first!