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Outdoors in Chişinău
This should be your first stop for anything outdoors-related. They have kayaks and mountain bikes and can tailor day or multiday trips in/on Moldova's many forests and rivers, sometimes dipping into Romania. Ask for Natalie or Alexandru. It's run out of a fantastic outdoor store, so you can stock up on supplies.
They also organise serious mountaineering expeditions to high peaks around the world.