I travelled to Merida from Belize on an overnight bus arriving in the middle of the night. We stayed at The Nest, a really good hostel which unfortunately has now relocated to Cancun. Merida is a city full of culture, head to the main square as nearly all attractions are accessible from there. We visited the Government House Art Exhibition, which depicts the history of the Mayans and their struggle for independence against the Spanish. The artwork is really interesting and the building itself is beautiful and can provide welcome relief from the sun. There is a large Cathedral on the square which is an interesting visit. The religious symbolism can be a bit overpowering but the architecture is worth the visit and if you get the chance to view it at night or see a wedding party, as we did, then it's certainly worth the visit.
The anthropology museum is a price spot for tourists. The walk there is a good way to see some of the city and there is street art on the way. The museum generally covers Mayan history but also contains history on local ruins and the origins of the Chinese community in the area. There are lots of people’s skulls on display that showed mutilation from prior customs (Apocalyto style things).
In the evening there’s a market and there are plenty of shops around the market, which are full of gift ideas, and are often made from local textiles and stone. The streets are cordoned off round the main square at night (I can’t say if this happens every night or just Saturdays) and the restaurants have live bands and dancing outside. It’s a beautiful sight and loads of locals and old couples salsa with each other in the streets. We ate at Amero. It's great for veggies as there is a really wide choice and they have live music whilst you eat, which is entertaining without being imposing. If you are only in Merida for one night I would say go for one of the restaurants on the square so that you can sit back and enjoy the music and dancing.