i went there and rented a room but the key says moist maiden its right next to the shop
The Black Dragon is above where the fisherman is (or was if you already bought his boat). IIRC there's a marker/star/twinkle at the entrance. If in doubt, click on shop markers. You can always back out and won't (normally) lose time for leaving a shop/business before interacting with anyone.
There's like a half-dozen quest-driven events that automatically trigger when entering/leaving a shop, but that's it and I don't think any of them relate to Daiyu/the Black Dragon. If you're worried about getting trapped into something you didn't want to do yet, Save before going inside and reload if you don't like what happens.
