As jib71 said.

(And welcome also to Flyertalk!)

My experience with 4 & 5 year olds is that they get tired of walking, and when they do, they are no fun at all.

How about a day or two in the Hakone park area as part of your itinerary?

There are cable trains, cable cars and ships you can all go on (get the 'Hakone Free Pass' - which isn't 'free' but will cover all the transportation costs in the area over a couple of days - or longer
http://www.odakyu.jp/english/freepass/hakone_01.html
and weekday pass: http://www.odakyu.jp/english/freepass/hakone_02.html ) This will let you cover a lot of ground with them without actually walking too much.

At the sort of budget you're looking at and with children, I'd personally go for a Japanese suite at the Takanawa Prince Hotel (you can often find them through Utell for about 30,000yen). The kids should enjoy the tatami'd space and the extra rooms, and they'll probably enjoy the gardens too.