We just got back from a week-long trip to Tokyo with 2 kids (3 and 6 years old).

Also looked for a place close to a Yamanote line stop.

We stayed in a "Premier" Twin room at the Karaksa Hotel Premier Tokyo Ginza for $225 a night (including in-room breakfast). The hotel is very conveniently located just 5 minutes from Shimbashi station (and next to the Ginza shopping street) - and the room was very well appointed and modern (but small - so it fit a Yoyo Zen stroller but anything bigger would need to be folded up). No park located close by though.