I have a couple of recommendations, based on one overnight experience at Chichen Itza and two at Uxmal. I'm assuming you are going to rent a car in Playa del Carmen and drive, and I would recommend using the toll road from Cancun to Chichen Itza. One stop along the way (but will consume some time) is a ruin near Valladolid called Ek Balam.
A "perfect" trip for me would be to get an early start from PDC, stop at Ek Balam, get into Chichen Itza late afternoon/early evening, get your ticket to enter Chichen that night (which should also include the night light show and the next day's admission); see the site the next morning, and drive toward Merida/Uxmal (going back to the toll road) that afternoon. Do the main ruin at Uxmal the next morning, and then the minor sites I list below that afternoon, spend another night in Uxmal, and then head back via Mayapan the next morning. You may not have time in your schedule to accomodate this, but it would be maximum Mayan exposure over the shortest period of time.
For Chichen Itza, I'd recommend staying at the
Archeological Villa. It is within walking distance of the side entrance to the ruins site, and is very comfortable and well maintained (at least it was a couple of years ago). They have an on-site dining room, pool, etc.
For Uxmal, I'd recommend staying at
The Lodge at Uxmal. Even though there is also an Archeological Villa at Uxmal (almost identical in architecture to the one in Chichen), we were not as impressed with the management of that property, and actually spent most of our meals at the Lodge.
There is a loop around Merida now (back when I first did this trip you had to go almost into downtown Merida to make the turn south) and I highly recommend it. Once on the southbound highway, you are on the
Ruta Puuc. In the vicinity of Uxmal there are some "minor" sites (Kabha, Sayil, Xlapa, and Labna) which are well worth turning into an afternoon (although you'll be a little rushed). I'd also strongly recommend a guide at Uxmal (we've done it both ways, and our guide pointed out stuff we had never noticed on our prior trip). I think you can self-guide Chichen Itza, but I've been there several times, so I may be biased (but it is the more restored and documented of the two major sites you mentioned).
Also, on your trip back, I'd also recommend stopping at Maypan. This is a later Mayan ruin site, and has some very clear murals, and well rehabilitated structures.
Hope this helps. I can provide additional information is you need it. PM me if I can be of further assistance.