If interested in the late periods at Ashkelon and the Near East more generally, there are two books I would recommend.
First, Early Islamic Syria: An Aracheological Assesment by Alan Walmsley. The author does a good job of outlining the history of the field, identifying important sites, describing the material culture and debating some of the most prominent research questions in the field of Islamic Archaeology. Overall, it is a good, fast,and informative read.
My second recommendation is Crusader Castles by T.E. Lawrence. Yes, that T.E. Lawrence. When he was 21, T.E. Lawrence spent a summer walking throughout Syria-Palestine and he visited every major Crusader castle in the region. He recorded everything he saw writing notes, drawing sketches and even taking photographs. A volume containing this material was published after his death in the 1930s. Recently, a new edition has been published and it is both a fascinating and interesting study. It is well worth your time.
Enjoy!