Congratulations! We will be celebrating our 25th next year by going to WDW, so there are lots of fun and romantic things to do whether you are just starting out or are an old married couple like us!
When we used to stay at Pop before we owned DVC, I always like to request the Tramp hotel (from Lady and the Tramp, nothing sketchy), and asked for a lakeside room - pretty view of the lake, and always got to see ducks and bunnies on our way out in the mornings. Quiet there too.
If we want to be away from the hustle and bustle of the parks (or like this trip, we don't have park passes) we love to go to the beach at the Polynesian at night and sit on lounge chairs and watch Wishes across the lake - they pipe in the music through speakers there, it's wonderful, and you don't have a crushing crowd as you leave!
We also love to just visit other resorts and take in the different ambiances. We have lunch at the Whispering Canyon cafe, then go relax in the Iron Spike room in the DVC section and sit in leather rockers or play chess/checkers. We always visit AKL because I love the gift shop and to see the animals (this trip we are staying at Kidani, so I can't wait). And doing the monorail loop without visiting parks, just getting off at each resort and wandering around is fun. The Beach Club, Boardwalk are great for wandering around, and we absolutely love Jellyrolls!
Enjoy! Hope you have many happy years and many anniversaries visiting WDW!!