We had many trips to Disney when our kids were babies. They are some of our best memories! As babies, they love to sleep AND they love just looking around. That makes for an easy/fun trip for the parents! We brought our comfortable stroller from home (double stroller/have twins) so we could recline the seats and put up the canopies when the babies wanted to nap. During nap time, DH and I would have a great meal with stroller and sleeping babies next to our table. One that worked really well that I remember clearly is eating in Italy in Epcot in the outside tables. We had adult drinks and an awesome meal. Some restaurants have congested tables so we'd stay away from those. We also enjoyed walking around Epcot countries and trying different drinks/snacks. When the babies were awake, a favorite was Chef Mickeys - just can't beat all the colors, music, and fun characters!
As far as rides, we always went on rides as a family. So whatever my babies, then toddlers, now teens are into at their age is what we went on. There were a lot of fun things to do when babies. We'd put them in our front carriers and go on many rides. DH and I still remember today how happy we were seeing things through their eyes! Enjoy trips like this because it changes once they're teens (lol). Now I have to take Bonine before the parks because they want to go on rides that make me nauseous.
Edit to add: We used to like going into Espn Club when they were babies. It's a little loud in there, but my babies were fascinated with all the TV's and weren't bothered. We also went to our resort hot tub at night with babies happily sleeping in stroller next to us. All in all, those baby trips were absolutely awesome!