I think the first time I went to Disney in Tokyo, I spent very little time at Disneyland with most of the days at Disney Sea. I've since gone back several times and that's still how the visits are allocated. Disneyland is a bit of a novelty because it's Japanese but, otherwise, I find it a bit dated (particularly in Tomorrowland). Disney Sea, on the other hand, is amazing and over-the-top.

If you're going to visit a shrine or temple, I'd suggest going to the Meiji Shrine in Shibuya, right by Harajuku. You can visit the Shrine (which is pretty cool) and then spend some time wandering Takeshita Street, which is not to be missed, if you enjoy people watching.

Another thing to consider is heading over to Odaiba and going to Sega's Joypolis, an indoor amusement park/center. I haven't been in a few years but some of the stuff is pretty wild. Odaiba is all-new, kinda fabricated, manufactured, but that's part of the fun of it. You can take the monorail over the rainbow bridge which gives great views or you can take a boat ride across the bay.

As another poster suggested, staying in Shinjuku for your Disney days can be a bit of a hassle. Some of the hotels in Odaiba offer a shuttle bus or, alternatively, there's decent public transportation access to Disney. My recollection is that coming from anywhere else, if you're making the train/subway transfer at Tokyo station, there's a ridiculously long walk in the station to connect.