I can't believe no one's replied to this yet
Congrats on your upcoming proposal. That's exciting.
There are SO many places, but how familiar are you with WDW? Some of these might seem obscure and unfamiliar if you haven't really explored WDW in depth.
At Magic Kingdom: Main Street train station balcony can be somewhat private depending on the time of day, and you still get a view of the castle. You can take a ride on the Liberty Square Riverboat. You can do it on a ride that only seats 2 like Haunted Mansion or Buzz Lightyear's Space Ranger Spin. There is a pathway off to the side of Cinderella's Castle connecting New Fantasyland to Liberty Square (to Sleepy Hollow) that is usually pretty quiet. The little boardwalk connecting Liberty Square to Frontierland can be quiet depending on the time of day. There is a pathway that connects Tomorrowland kind of behind Space Mountain to New Fantasyland (where Toontown used to be - it runs between the train tracks and Tomorrowland Speedway) that's usually really quiet. In between Uptown Jewelers and Crystal Arts on Main Street there is a little area that goes off to the side that stays pretty quiet. There's also a pathway past the boat docks to the left of the monorail in the front of the entrance area that leads out around the Seven Seas Lagoon a bit that hardly anyone goes. Or take a ride on one of the water taxis TO a resort from MK during early visiting hours when there won't be anyone on the boat (everyone will be going to the park not from it to the resorts).
At EPCOT: The pathway from Test Track to the Odyssey (it can be very beautiful with flowers and over the water and the monorail passing by). Before World Showcase opens when everyone is going in that direction, go to the World Showcase Plaza at the front all the way to the water. When World Showcase first opens, go straight over to the United Kingdom to the garden in the back or to the garden pathway in Canada (it's very pretty). You can even go farther into Canada to the little waterfall by Le Cellier and O Canada. There is a terrace between the pathway connecting the United Kingdom to France that's usually really quiet. You can walk down to the lower level by the water. There is a gallery of Arts and History in Morocco that has a beautiful tiled atrium that can be fairly quiet depending on the time of day. The terrace in front of Italy on the water can be quiet and has an excellent view of Spaceship Earth across the water.
At Hollywood Studios: There aren't too many romantic private places here unless you go straight to the back at park opening to the Streets of America. You could go straight to the exit area of Tower of Terror at park opening (since everyone will be going to the entrance). It's a nice secluded area. If it's open, go up the pathway to Fantasmic! during the day when no one would go that way.
At Animal Kingdom: The Discovery Island trails around the Tree of Life. The Pangani Forest Exploration Trail or the Marharajah Jungle Trek trail. There's a pathway that connects just past the main bridge from the Oasis to the bridge by DinoLand USA.
At the Resorts: Grand Floridian - over by the Wedding Pavilion of course. Polynesian - the beach. Contemporary - I heard the California Grill Lounge has a great view of MK and the fireworks. You can even walk along the piers in the back on the water. Boardwalk - go in the early afternoon when everyone else will be at the parks. Find a nice spot. You might be able to go on the little balcony area of the Atlantic Dance Hall right on the water. Yacht/Beach Clubs - on the beach maybe on one of the cute wooden swings.
Downtown Disney: Go in the morning when not many people will be there. Any little spot by the water. The bridge crossing to Fulton's Crab House or the area in front of that sometimes has nice flowers. The boardwalk/pier winding behind Paradise 37 by the boat dock and the path that follows along the edge of the lagoon. There's a path that goes from the back of Cirque du Soleil out to the far parking lot that has a nice view of the lagoon (although with the parking garage construction I don't know if that's still there).
That's all I got
Good luck! I'd love to know where you chose.
