Here’s one more as the equipment at Kinshi Park 墨田区立錦糸公園 looks very appealing and there is a range of hotels very close by.

Lotte City Hotel is right between Kinshichō Station and Kinshi Park. It’s a decent 3 star hotel with some larger deluxe rooms that nudge it into the upmarket territory the OP is seeking. https://lottecityhotel.jp/en/room/luxi.html If either of the kids (or parents) is wild about Koalas, this hotel has that passion covered.

Not quite as perfectly positioned but still doable, there is the Moxy Hotel Kinshicho that comes under the Marriott umbrella which is a little to the South. Otherwise there is a Sotetsu Fresa a Tobu and a Super Hotel in the vicinity in the reasonably priced category.

Kinshichō is a JR station on the JR Chuo line 3 stops away from Akihabara.

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.

That's steep for that category of hotel. I paid roughly that much before taxes at the GHT earlier this month.