At Saratoga Springs, Port Orleans, and the Wilderness Lodge you can go on a horse drawn excursion. It's very nice. Very relaxing.
As everyone else wrote, put it on your resort and dining reservation. We generally go to WDW for our anniversary. At Tony's, the sprinkled the table with mickey confetti. The waiter made an announcement to the entire restaurant that it was our anniversary...and he had them wish us a happy anniversary.
At Nacrossee's they gave us personalized menu's.
Go sit on the Poly beach! Since you'll be staying there. And watch Wishes. Very romantic. Plus before hand they have the Electrical Water Pageant. Check with the Poly front desk, but I believe it's about 1/2 hour before Wishes. Grab a drink and or dessert and enjoy the fireworks.
The important thing is to also find your own magic...spend some time on Main Street after the park has closed with little or no people there...do the same at Epcot after Illuminations...or take a walk down the Poly beach to the Wedding Chapel at the GF.
Happy Anniversary!!!