What I did last time I was there on a cruise was to take a local bus down to The Europa Point Lighthouse, the WW2 Sikorski memorial
and the Shrine of Our Lady of Europe.
Then wandered back up the west side of the peninsula, where the locals live and went to the Europa Waterfall, calling into the Cathedral on the way back.
A low key sort of day, with various other sites and cemeteries of interest especially to a war historian like myself.
I'd been there before under my own steam on the coastal bus and done the usual tourist trail up the rock etc.
Several of the bus routes almost reach the port on their way to the bus station, and a day bus ticket on the comprehensive network is £6.60- https://www.gibraltarbuscompany.gi/bus-network-map/