I had similar problems searching for hotels in Tokyo (and elsewhere in Japan) for my family. Finding suitable accommodations was not as simple as I hoped.

How old are your kids? Mine are teenagers and for me, I eventually chose 2 connecting rooms at hotels, one for my wife and I and one for them. This obviously may not work if your kids are younger, but hotel rooms in Japan are noticeably smaller in comparison to Western hotels. Cramming 4 people into a hotel room anywhere is uncomfortable, do you really want to spend 4 nights in tiny room with 4 people? From your post it looks like you are considering this. For me, this quickly did became the only option. Be aware that unlike Western hotels, you need to have all people be identified. You can't rent a room and cram 4 people into it when you've only told the front desk you have 1.

You can find Western chains easily in Tokyo, but for our Tokyo stays we eventually decided to stay here.

http://www.jalhotels.com/domestic/kanto/yotsuya/

It is a business hotel, chosen only because Japanese friends of ours with similar aged kids stay there and suggested it to us. So, fewer frills than Western chains, but less cost. I think our cost was around 100-120$ a night per room. When I needed a night at Narita I went with the same chain, sent emails requesting (and receiving) a guarantee of a connecting room, and the cost was 100$ a night per room. For our family, we chose to spend a little less on a room so we could have a little more elsewhere. (This isn't as big a deal when it's just 1 or 2 people, but when all food/additional costs are multiplied by 4 every 100 yen saved adds up over time).

There are many threads covering business hotels both in the Japan forum as well as the Budget Travel forum so you can find other recommendations as well. Good luck.

dcman2