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There are a lot of caves around the island, though none of them are particularly impressive. Some cost money and may have optional guides. You can find them using the map or signs on the island.
The domain of the endangered Cat Ba Langur, of which there are supposed to be only around 100 left. Things on offer include a walk to a peak viewing tower (1½-2 hr round trip; slippery and muddy if it's rained recently), a frog pond (probably better in the off (wet) season), a short nature walk near the frog pond, more stuff which you can probably find online.