Google Maps and Wikimapia don't know about 松島城 (Matsushima castle).
I would start to doubt its existence if it were not for the numerous pictures available:
It has a view on Matsushima Bay.
What are its latitude and longitude?
I also find it incredibly difficult to search for a lot of things in Japan, especially in English on Google. Having the exact Japanese name and address makes things easier.
This tower is actually not a "Castle" but rather a "castle style tower". It is an observation/look-out tower.
Here is the address: 松島城天守閣天望台 〒981-0213 Miyagi-ken, Miyagi-gun, Matsushima-machi, Matsushima, Chōnai
I don't know much about it, perhaps it is hard to find on Google because it isn't really (historically) significant... ? I did find one blog post on the internet that mentions it: https://smoloney.wordpress.com/page/3/
edit: another link with some discussion on what this structure might be