Although we have never eaten at Yachtsman, I think Le Cellier is a nice restaurant for an anniversary. We celebrated out 10th anniversary at WDW earlier this month and had a wonderful meal at Le Cellier.
We had our *actual* anniversary dinner at 1900 Park Fare - and it was a bad experience. We didn't note our anniversary on all of our reservations - just the actual day at Park Fare. However, we did wear the "Happy Anniversary" buttons all week long. When we checked in at Le Cellier, they noticed the buttons and treated us like royalty. They also gave us a certificate stating it was our anniversary with all of the staff's signature. The host staff and wait staff spent a lot of time chatting with us. The food was great and it was just a wonderful meal. We were seated at a 2-seater table and found that we could converse without a noise problem. It was romantic in the sense that we had great food, good company, wonderful service and outstanding ambience. By far the best meal we had all week!