Limassol Medieval Fort - Cyprus Mediaeval Museum - Near the old port
Built in the 14th century on the site of an earlier Byzantine castle it houses the Cyprus Mediaeval Museum. It was here that, according to tradition, Richard the Lion-heart married Berengaria of Navarre and crowned her Queen of England in 1191. 

Municipal Folk Art Museum - 253 Agiou Andreou St.
A beautiful collection of Cyprus Folk Art of the 19th and early 20th century is exhibited in a restored old house.

Limassol Municipal Art Gallery - 5 Vyronos St. (near the Public Gardens)
The art gallery houses a representative collection of paintings of well known contemporary Cypriot artists.