You probably will bring your stroller to travel with your baby, and where will you visit in Japan? Mainly within the city or the peripheral? If you travel within the city, then you will need to ride a lot JR and metro, if you travel in the peripheral, then I would suggest you consider rent a car.
From my experience in April, I brought 2 kids, one is 2 yrs old and he needed a stroller, it was so hectic in travelling on JR because most platforms were lack of lifts to go up and down. In particular we have 2 children, this bothered us a lot.
Furthermore, if you travel by JR, the system is very complicated, so you need to do a lot of planning and research into the routes and train schedule. Just be prepared to do all these. If you are willing to spend time on this, free touring is definitely more enjoyable.
I plan to go 大阪in end Jul with my 6 yrs child. Can anyone tell anywhere is good to them other than Universal Studio ? Any zoo or special places to go ?