Hi David,
I live near Banff and have done lots of backpacking trips in the park. There are so many great hikes but one I think you might enjoy is a loop near Lake Louise including Paradise Valley, Sentinel Pass, and Larch Valley. It’s not a particularly long backpacking trip (20-40 km depending if you add on a few side-trips and make it a full loop rather than catching a ride back to your car). Mostly, I’d recommend it because it features some of the most beautiful scenery in the park and it’s quite romantic (something that, from the sounds of it, might come in handy).
I would start at the Paradise Valley trail head, then leisurely make your way up to camp at the Paradise Valley campground. If you like great views and the weather is good, wake up early the next morning and go up Mount Temple. Temple is the heavily glaciated peak that dominates the entire area but the route is non-technical apart from some scrambling. Ascending Temple is a fairly full day. Return to the same campground for a second night then go over Sentinel Pass into Larch Valley the next day. Labor Day might be a bit early for the trees to begin changing color to a vibrant yellow, but it they are it’s beautiful. Add on a side trip to Eiffel Lake and when you reach Moraine Lake, take some time to wander along the lake shore to enjoy the impressive Valley of the Ten Peaks. If you’ve just popped the big question, you might want to book a night at the Moraine Lake Lodge. It’s quite romantic. You can then either walk back to your car along a simple trail through the forest or it will be easy to flag down a ride.
Labor Day will be a busy time in most parts of Banff and the area surrounding Lake Louise is quite popular. During the day there will be lots of people on most trails (those that you could do in 2 nights anyway). Most of the crowds are day-hikers, though, so early in the morning and in the evening you should be able to find some tranquility.
You can google trip reports and find youtube videos on this loop. I can also scan a description from one of the local guidebooks if this hike sounds interesting to you.
Enjoy your trip!