You've mentioned three of my favourite places in the world: Merida, Chichen, and Uxmal... But to do them right you need at least most of a day to reach and see each. Chichen is about halfway between Merida and Cancun and not something I'd want to try if I had a ship to catch later in the day.
To truly explore and enjoy either Uxmal or Chichen, you need at least a half a day. They are magnificent and awe inspiring. If you like art, history, photography, and/or culture; you definitely would want to spend time to see all the structures. There is variety in them so it's not like you walk through the gate, see a couple and go.
Chichen is one of the biggest Mayan sites (something like 1.5 by 3 miles in size). There is an older section which has the Observatory and the section where you enter that has the Castle, which are two of the most shown (in photos) structures.
Something to check into if you want to see a ruin site:
There is a smaller and older site called Dzibichaltun which if I remember correctly is just off the road between Progresso and Merida. It only had a few structures when I was there so it is more of a "look and go" site.
Merida is an awesome place. I loved bartering in the old market. Unless it has changed since I was there, a person could spend half a day, browsing and bartering.
As for shopping, I love the bags and clothing I got at a Miro Store in Coz. The company is based in Merida, I think, so you should be able to find at least one store. Symbol (logo) is a toucan bird on a white background.
There is a photo of the bags on this thread:
Have a great trip.