The plaza and church are must do visits when in Las Palmas but are better done without expensive tour options.
Walking from the cruise port means turning right and walking along the coast until you see the church and Old Town (about 80 mins walk) or catching one of the many yellow buses along the coast to them (about 15 mins). Directions on where to catch the bus can be easily obtained at the tourist info office at the exit of the cruise port.
Once visited head down the hill to the lovely shopping street with Zara etc. The Benetton shop here sells Jean's from as little as €3.50 a pair. Walk to the end of this street to the quaint little church and bus station. At the bus station catch the #1 bus marked 'Puerto' back to the cruise port. Just before the cruise port there is a sharp bend to the right taken by the bus. This is the lovely beach area and if you get off here it is only a 10 min walk back to the cruise port. Highly recommended!More