Your lucky day...I have a '99 Millenia S and my father has a '96 Millenia S. My sister also has a Millenia, but not of the S variant...which to me makes it a substantially different car in many ways.
I bought the S after needing to get rid of my SUV ('02 Yukon) for something that got better gas mileage and not having to worry about putting high mileage on it. I bought it with 29K miles on it and I gotten the odometer up to 81K.
Overall the car has been great. For the money you really can't get a nicer ride inside. Mine has everything from heated seets to a Bose Stereo...yet it was cheaper than a Maxima or Accord from the same year. the car has a fairly good composure and I personally think it looks really nice (esp. with the '99 17" 5 spoke wheels). The ride is very smooth when driving over relatively flat terrain. People always complement me on how smooth the car is.
Now for my complaints... Although the car is very smooth when the terrain is smooth or just marginally bumpy, the ride quality quickly deterioates when the road gets coarse. It really is annoying sometimes. Also, the transmission just plain s*cks. It takes forever to downshift and results in very annoying jerks when it does after mashing the pedal. This car would be infinitely better if a 5 speed was ever offered.
I have done a lot of the maintenance on it myself (spark plugs, fuel/air filters, etc.), but this is not an engine you will be doing any of the biggers stuff on (timing belt, auxilary belts, etc.) as the engine is unbelievably packed with the supercharger. Because the engine is difficult to work on, it is even more expensive to have fixed. The local mazda place charges $500 just to do the timing belt.
The only mechanical problem I have had is that one of the coil packs went bad on one of the cylinders. This is one of the newer designs where each spark plug has its own Coil instead of having the traditional coil/distributer setup. It caused the cylinder to misfire occasionally. The coil was a $300 replacement.
One last gripe is that the tires for the OEM 17" wheels are a bit pricey because they are low profile. You can pick up a set of 4 Continentals at Tirerack for around $400 and have them mounted fairly cheaply, but if you go to a local place they will most likely try to charge you well over $550 before you get out of there.
Now that my company is moving and my 45 minute commute will be reduced to less than 10, I will probably be getting rid of my car and getting a much needed truck (my lifestyle of driving up to the mtns, kayaking, and biking requires this and has limited me over the last year or so). The car will have treated me well, but I probably would not buy one again. This is not a car to have for the long haul. The engine is too exotic and pricey to fix. I've heard it costs at least $2500 to replace the supercharger if it goes...no thanks.
My Dad's Millenia S has 100K on it and is still running well. He takes very good care of it and always does all needed maintenance on it. He has had it from day 1 which I think helps and drives it carefully. The only problems he has had have been trim issues like the "wood" in the dash cracking near the drink holders and the CD Changer breaking (which he got fixed).
I hope this helps you make a decision. If I were you I would probably skip it and get an Accord or Maxima from the same time frame that will be easier to maintain.