Is this first week in May (golden week, kids are off school and areas frequented by teenagers are extremely congested) or another time in May?

If first week, be aware that getting around popular-with-young-people locations is going to be particularly difficult with a baby stroller. Getting around with infant carrying wraps/harnesses are (certainly if you are already used to them) much easier and what you`ll find most local parents using in Central Tokyo. What area is considered an optimum place to stay will likely vary according to what time in May you are going and whether you will be pushing or carrying the 12month old. If you are taking a stroller it would be best if it folds up as minimally and easily as possible, they vary, but the storage area in the back of a taxi may be smaller than you are used to.

I am not particularly familiar with all the hotels in your impenetrable list. My suggestion is to cross check the location of each of them using Google Maps with the parks and play areas that get highlighted using “children’s playground, Tokyo” as a search term. Take a note of the hotels that are close to a Metro station, close to a playground and close to an area you want to hang out in.

As someone accompanying an infant you will need to take your shoes off and put them back on even more than other visitors. Try and avoid shoes you can’t remove/put on whilst holding your child during an uncooperative moment.

I cannot even imagine how one would tackle Kyoto in Golden week with a stroller.

ETA - this thread from a couple of years ago has some suggestions. I just tried chatGPT to see what it could come up with and it was close to useless.
Tokyo accommodation with Toddlers