If you want to do something different this is different but would need a car or taxi. It’s a unesco world heritage site.
Never understand why it’s not cruise ship itinerary unless to preserve the site
http://www.mcw.gov.cy/mcw/da/da.nsf/All/4EF92D50616EFE49C225719B00314171
In Limassol itself there is the marina as well but don’t know how far from the port. There are lots of cafes but again not sure where in location to the port. There is the old carob mill area which you may find interesting but I don’t know what it’s like post covid. I know Larnaca like the back of my hand but Limassol less!