What's your budget? If you're looking to keep costs down, the Toyoko Inn group has a big chain of medium-sized no-frills hotels all over Japan, and they do family rooms, buffet breakfasts, have laundry facilities (very handy if travelling with a toddler) and so on.
But if it's likely to be a one-off trip to Japan, I'd really recommend staying at least a night or two in a traditional ryokan to get a taste of traditional Japanese-style living. There aren't many ryokan in Tokyo, but lots in Kyoto, and if you only have a week, then splitting it between Tokyo and Kyoto (new v old Japan) would make sense.
On our last trip to Japan last year (we used to live there and go back to visit most years) the DCs and I spent a couple of nights in this place - Yoshi-ima Ryokan - which is a traditional but foreigner-friendly ryokan right in the middle of Gion in Kyoto. We had a huge tatami room, divided into two, with private bathroom. One good thing about the Yoshi-Ima as far as I was concerned was that you can opt to just have bed and breakfast, rather than dinner being included in the room rate as at most ryokans - we're vegetarian, and most ryokans don't cater for that. It also worked out cheaper to eat out, and gave us more flexibility with timing, as ryokan dinners are usually quite early. But we did get a full Japanese breakfast served in our room, which was great.
The cost of return shinkansen tickets Tokyo-Kyoto is usually a bit more than a week's Japan Rail Pass, which makes it worth getting the pass as you can also use it on overground trains in Tokyo and some other short excursions (though bear in mind you can't use the rail pass on the very fastest, newest shinkansens to Kyoto).
I agree that everything in Japan seems very expensive these days - I remember when it was Y200 to £1, but now it's more like Y140. Hundred-yen shops are still good value, though (like pound shops but much, much better).