I brought my family to Japan when my younger son was 1 year 1 month. Walking to the top of Himeji Castle with him in a baby bjorn might be one of my greatest physical accomplishments.

We stayed in western hotels - places like Prince Gallery in Tokyo (on points), Westin Kyoto, and Sheraton Hiroshima - do not remember having to pay extra for a crib (though the Sheraton wanted extra $ to put sheets on the pullout couch for our then 8 year old).

Shinjuku might be a little flatter to the hotels from the station vs. Shibuya but you should be ok with the stroller in general. There are a bunch of places near Tokyo station too that would be relatively central.

I think I visited the Gyoza Stadium on that trip with the stroller and kids - but can’t speak to many other dining experiences with kids as we ate at more larger or chain restaurants (my wife and her mother were on the trip with us and loved Japan - but not so much Japanese food + we looked for places with highchairs). I do visit Tokyo 3x per year so I think you will find plenty of places to eat, but some of the ones you might really want to try might be a tight fit or not have highchairs.