Just saw this - if you haven't left already, just wanted to say that you should have a great time with a baby in Japan - people usually love western babies and make a huge fuss of them.
Japan is generally pretty baby-friendly - you can take them to pretty much any restaurant, though at that age I'd recommend either Japanese-style ones with tatami seating areas (you can just lie the baby down on a blanket next to you as you eat), or larger ones where there is room to take a buggy in with you and park it by the table. There are lots of tiny restaurants where one buggy would block the only thoroughfare, so you'd end up juggling a baby on your lap the whole meal. Few restaurants have high-chairs, and the ones you do find are usually only suitable for older babies and toddlers (hard wooden seats and nothing to strap them in with).
Yes, you can take a buggy on the trains, and the majority of stations now have lifts to make access easy. I wouldn't recommend travelling with a buggy before 9.30am in Tokyo though. To go on buses you will usually need to fold the buggy up. When my two DCs were that sort of age (and we were living in Tokyo) I used a combination of baby bjorn and a lightweight folding buggy with a strap to carry it over my shoulder - useful for buses and also for the stations which do still have stairs and no lifts.
I did try once or twice to use a car seat in a Japanese taxi, but failed - the seatbelts seemed to be too short to fit around it. When I had to take taxis I usually ended up putting the baby in the sling and putting the seatbelt on in between me and the baby. Not ideal, but (I think) better than just holding them. Tokyo taxis rarely build up much speed anyway....
Japan is also pretty BF-friendly, with feeding rooms in department stores and big stations. Many Japanese women seem too shy to BF in public except in very child-oriented places (playgrounds etc) but I never had any negative reactions when I BF in restaurants, on buses and so on.
Nappies can be hard to find in central Tokyo or business districts, but obviously widely available in residential areas. Look in larger pharmacies, supermarkets (the non-perishables and household goods are often on a different floor from the fruit & veg etc) or children's sections in department stores. There are also loads of branches of Toys R Us or Babies R Us which stock nappies, and another good place is a chain of baby and children's discount stores called Akachan Honpo.