There's a small museum at Zia, which often displays a nice bunch of older pots and ancient artifacts. There are a lot of pottery artists there, and the Zia bird with two tails seems to be a favorite theme, though a lot of traditional motifs are used. Lots of red and black on white backgrounds, some flowers, etc. Christmastime is a good time to visit because there are Pueblo dances on or just after the holiday.
Santa Clara is pottery heaven, expecially if you like the shiny black pots that made the it famous and have some dough to spend. One of my first serious pieces of pottery was from there...a Margaret Tafoya bear paw print pot I bought at auction in Chicago. The master of the highly detailed miniature pot, Joseph Lonewolf, is from S C and his pieces stand alone in Native American pottery...unique, except for those who copy or follow his lead. Amazing. I bought a red Nancy Youngblood pot a few years ago, and she's one of the greatest younger potters with her own distinct style...a swirling ridge design that is simple, almost contemporary style, and hypnotizing. There are more great potters there than I could mention. There are interesting but modest cliff dwelling nearby if you visit. Puhyay, I think.
It's pretty hard, in my experience, to visit Jemez...they're pretty private...except on the occasional feast day or getting "smuggled in" by a craftsperson you're buying from. A lot of artists have little shops and galleries near the road in or at the vistors center. If you get a chance to go to the old village, do it..it's in a pretty cool canyon. They're well organized there, so you can see a lot by visiting or contacting the visitors center to see what's up. They do a show near the visitors center in early December that has a lot of great pottery and other things. There is also a website...jemezpueblo.org
My favorite Pueblo to visit will probably always be Acoma...Sky City...due to it's spectacular location. I always tell people to skip the casino...go to the Pueblo. Its a remarkable place, and I think they're almost thru restoring the ancient church. You can stand on that mesa, look all arond the valley, and you could be back 400 years...or more. really cool.
I probably do more business at Santo Domingo than anywhere else, but there's no visitors center and few amenities outside of some small artists shops around the plaza as you go in. They're famous for shell and stone lapidary work...heishi, inlaid and overlaid shells, necklaces and earrings, etc. without a lot of silverwork. There is pottery there too. Mostly geometric designs, a lot taken from prehistoric pieces.
If you're wandering the Rio Grande, DO visit pueblos. Some might be a little, um,
underwhelming, but there's interesting art in almost all of them. Just be polite and respectful of customs...a little research in advance is a good idea...because it's not a theme park, it's peoples real lives and cultures. Some are a lot more photogenic (or even permit photos) than others. I'm amazed at how many long time NM residents have never visited...but there's always a first time. A visitor could build a whole trip around covering the various places. Bring money! Buy Art! Have fun!
This is a good place to start:
New Mexico Tourism | Native America | Pueblos, Tribes and Nations Acoma Pueblo