One block north of the square is the Museo de Comayagua (8:30 a.m.–4 p.m. daily, US$1), facing the Plaza San Francisco [1], in a 16th-century building that was Honduras [2]’s seat of government for a short time in the 19th century. There is an interesting collection of pre-Hispanic pottery, as well as well-done exhibits on local culture and traditions. Labels are in English and Spanish.
Links:
[1] http://www.moon.com/destinations/honduras/central-honduras/comayagua/sights/the-colonial-center/la-iglesia-de-san-francisco
[2] http://www.moon.com/destinations/honduras