If you're looking for the traditional "Cantina" experience, do NOT leave Merida until you hang out at La Negrita. Its super casual atmosphere (there's literally a tree growing in the center), affordable drinks and live music make for a great evening night out or even a chill afternoon.
More into wine vs. margaritas? Well GET LOST, you're in Mexico! Just kidding, of course. Oliva Patio is a chic place to get into the European vibe. Best ambiance in the evenings, they have a great wine list & small plates, including some local Mexican wines.
30 minutes from central Mérida (and less crowded than Chichén Itzá), Dzibilchaltún is known for its Temple of the Seven Dolls. Alongside the ruins is an impressive cenote that was once the site of a Mayan religious cult and is today a popular spot for swimming.