Beside the 7-Eleven shop in Banli is a very short row of four restored Qing dynasty stone-and-timber mansions. One of them is open to visitors as an unstaffed museum, and is worth a quick look if you're passing. Just across the road, take the passageway beside the tourist office to reach an arc of sandy beach that's pretty but unsafe for swimming most of the year.
Beside the museum, a trio of old buildings operates as a 13-room guesthouse (d/q without bath from NT$1400/2000). Conditions are somewhat basic, but there's a reasonable sense of historical authenticity. Make advance arrangements as there's no reception.