Not to be confused with Nagoya Castle in Nagoya, this castle was the launching point for invasions of Korea during the Sengoku Period. Today the castle walls are all that remain. It's still pretty nice, and there's a modern museum on-site.
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七ツ釜
Also in Minato is this group of seven caves, formed by the tumultuous Genkai Sea. Accessible by bus, with a bit of a walk from the main road.
立神岩
Located in the town of Minato, a scenic group of standing rocks along the coast. Can be accessed by bus.
高島
Not to be confused with the nearby Takashima (鷹島) in Nagasaki prefecture, this island in Karatsu Bay is dominated by a large hill, and is accessible by a ferry that leaves from the jetty near Karatsu Castle. There's a small village on the island with some picturesque little garden plots, as well as a shrine thought to bring luck in winning the lottery. It's possible to climb the hill to its summit via a well-marked and not terribly strenuous path, which offers nice views of Karatsu and its surroundings on a clear day. It's no longer possible to walk or bike all the way around the island, as a significant section of the road was blocked off due to a landslide. Interestingly, most villagers on the island have the surname of "Nozaki". Bicycles can be brought along on the ferry for an additional charge, but the island is walkable without one.
曳山展示場
The floats of the famous Karatsu Kunchi Festival are all on display here everday except during the festival. They have informative English descriptions about each float, what it is, when it was made, and sometimes why it was chosen to be a float.
河村美術館
The museums houses a collection of paintings from the 19th to early 20th centuries.
唐津城
A 1966 reconstruction of the former castle.