The park is open 9:00 to 17:00 (sometimes 18:00), closed on Tuesdays. Admission is 200 yen, and rides are pretty cheap (200 yen for adults per ride, 100 yen per ride for kids). Access is via the Toden Arakawa Line streetcar; get off at Arakawayuenchimae.
As of early last year, there were over 20 medium and large-sized train museums in Japan; three of those are in Tokyo. No train museum in Japan compares to The Railway Museum. But the Tokyo Metro Museum and Tobu Museum both hold their own and offer something unique.
The Tobu Museum was larger than expected and pretty fun! I spent about two hours getting through the whole place; the Tokyo Metro Museum only took about an hour.
Open from 10:00-16:30, except Mondays, the museum admission is 200 yen. It's located directly beneath Higashi Mukojima Station on the Tobu SkyTree line. Note that not all trains stop at the station. Most times you'll need a local train. If the giant Railway Museum in Saitama is going to be too much for your family, this is a great alternative, and those who love trains should plan on stopping here as well.
It's possible to do all three train museums in one day, but note that railway museum in Saitama is very large and three train museums could be train overkill.