It is called the Pilgrim's Monument and was built in 1907-1910 to celebrate the landing of the Pilgrims in the 1600s. You are right though, according to wikipedia, it's designer did model it after the one you mentioned in Spain! It's supposedly the tallest all-granite structure in the US.
OMG!!!! We just got home last night around midnight from 4 days in Provincetown!!!! It was our third time up there and it was fabulous! We arrived the day of the big Portugese Festival and the Blessing of the Fishing Fleet. They had a parade down Commercial Street. The weather was unusually muggy. It would be crappy in the AM but gorgeous in the afternoon and I had two perfect days on the beach. We got up yesterday morning, packed the car then spent part of the day on an actual schooner for a two hour cruise by sail out in Cape Cod bay. It was amazing how far away we got from P-Town but could see the Pilgrim Tower looking as tall as a Supertall that far out in the water. As we came back into the harbor we buzzed real close to the actual tippy tip of Cape Cod and people had boated out there to lay on the beach. Amazing!
I'm feeling a bit depressed today because I wish I was still there...although I was getting rather hostile driving home last night. A seven hour car ride is not for me.
Nice pictures. I've never made it that far north up the Cape before, and I'll have to see it some time. Provincetown looks much denser than the places on Cape Cod that I'm familiar with (Orleans, Chatham, Harwich, etc).