The port of Las Palmas is one of the busiest in the whole of Spain, never mind the Canaries. It is conveniently situated very close to the city centre so whether you are a cruise passenger or a scheduled ferry passenger you can soon be in the center and from there anywhere else on the island.
It is possible to sail to most of the other Canary Islands but I regret the fares are “disappointing” to be polite! Look out for special offers on all routes!
As for the weekly route to Cádiz in Andalucía, Spain you may be interested in this account.