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Located on the grounds of the Taga Shrine, this is essentially a three-story sex museum devoted to fertility and its graphical expressions. Two of them are found in the name: the kanji 凸 and 凹 usually mean "convex" and "concave" respectively, but the shrine's logo makes things clearer by placing the pointy bit under the one with the gap.
多賀神社 Taga-jinja
Although Taga doesn't get much press at the local tourist office, it's probably the most unusual sight in town: the shrine is an ancient Shinto fertility shrine, full of phalluses of all shapes and sizes, including a mighty carved log that gets carried about on festival days. It's on the north side of the river, not far from the better known Warei Shrine.
宇和島城 Uwajima-jō
Uwajima Castle occupies a strategic location at the heart of the city. Unlike most Japanese castles, it's actually an original (dating to 1665), not just a ferroconcrete shell. That said, the castle is comparatively small and modest.
和霊神社 Warei-jinja
A large, comparatively staid Shinto shrine, probably Uwajima's best-known attraction among the Japanese. Not worth a detour, but you'll be passing by on your way to the Taga Shrine anyway.
宇和島市立歴史資料館 Uwajima Shiritsu Rekisi Shiryōkan
One of the first Western-style buildings in Ehime Prefecture, it serves as a museum dedicated to the history of Uwajima. It is designated as a Registered Tangible Cultural Property.