Not much luck in the ubeda forum.does anyone know if many things are closed there on a monday? Museums,restaurants etc
There are museums and museums. The ones that are run by local government tend to have day off on Mondays. Others may vary times so better to visit the local tourism web site to study.
For example the famous Holy Chapel of the Saviour or Sacra Capilla del Salvador is open for visits on a Monday
Plenty to enjoy on a Monday in Ubeda and just depends on whether you are visiting to see for example the building of San Juan de la Cruz which is closed.
Also I would take the opportunity to see Baeza as well if staying in Ubeda.