One of the most popular day trips from Meknes is to go visit the famous Roman ruins of Volubilis.
The site is enormous and really gives an idea of the lifestyle in this Roman outpost that was essentially used for its military position and olive production.
Most of the monuments were unfortunately damaged when Moulay Ismail needed building materials for his palaces in Meknes but there are over a dozen great mosaics to be seen. If you want to know more about 2000 year old Volubilis please see the official site : http://www.sitedevolubilis.com
There aren't many hotels near Volubilis so most people decide to stay in Meknes.
Transport is not a problem,it is only about 20 km and taxis are very cheap. We can even find you a taxi for the day if you wish. A cheaper alternative is to take collective taxis and then it will only cost you a few Euros.