YolkSac
You need to do a lot of walking in Tokyo - cos cabbing is expensive and I reckon you will be taking a lot of trains as well.
Perhaps you can get an umbrella lightweight stroller as temporary measures. I got mine from KidsMall at around $49.90 few mths back, very lightweight that it can fit into my 1.2 litre, almost bootless car.
If you are staying in Shinjuku area (basically shopping area), you can either take train or take direct airport transfer via coach (though there's jam, but good if you have few luggages to manage). I still have the Tokya Train map in softcopy, let me know if you need me to email to you. Near the Shinjuku train station, you can sign up for day tours or short trips in and out of Tokyo.
Fish market
Popular place for most tourists (sadly this is the only place that I manage to go in Tokyo, other than airport/hotel/office). It's open from 5.30am to 1.30pm and many people actually reach there earlier to catch a glimpse of fish auction, followed by a sumptuous raw sushi (yummy, I enjoyed sushi more than the auction)..
Popular Suzhi shop recommended by my colleague at Tsukiji (fish market), nearest train station is Tsukiji, exit A1. But be prepare for long queue, at 6am we have a long queue of 20pax ahead of me, but that's the best sushi I have ever tasted, it really melts in your mouth. You can also cab there from Shinjuku at early hours without jam (around 20mins). I have the softcopy of the directory to fish market, if you are keen.
http://www.tsukijigourmet.or.jp/17_daiwa/index.htm