Monday to Thursday head out of town. Any visit to Yucatan should include the Ruta Puuc Ruins and Chichen Itza. Get an early start so you can avoid the crowds and the sun. Have a leisurely lunch and decide whether you´d rather spend the afternoon exploring the ruins or floating in a cenote. If you are going to be spending time on the Caribbean don´t bother with the gulf coast beaches. You might want to see the flamingos up close in the lagoons around Celestun so you could lunch on the beach in that case.
Monday is not the day to see the churches though as many are closed. Have lunch along the way in one of the restored haciendas and drinks at sunset in another. When you get back to Merida there is something planed every night of the week from free music concerts to folkloric dancing. Dinner can be taken late in Merida so you even have time for a quick nap after your day out of town.
Monday Night at 9pm the Ballet Folklorico de Merida and the Orchestra Jaranera perform the Vaqueria in the Zocalo the traditional dances of Yucatan that developed in the 18th century on the haciendas and cattle ranches.