Ruths, there are some who believe the radiation problem is worse than being reported and the government is involved in a huge cover-up. Even IF you believe them, even IF they are right.... the levels of radiation recorded are not immediately dangerously high.
Time and distance are your friends when it comes to radiation: the further away from the source you are the lower the level of contamination. The less time you are close to that source the lower the level of contamination.
This will work for your daughter on her visit: Osaka was far enough away from Fukushima so as not to be affected.
From what I can tell, Tokyo MAY have hot spots of radiation around, but not everywhere and not high level.
The greatest concern is that the food and water chain may have been contaminated sufficiently so that there will be a LONG TERM affect on residents.
I'm no nuclear physicist, but personally I'd have no qualms about a short visit to Tokyo. I'd tried to check my food wasn't from Fukushima prefecture, but otherwise I'd be happy to go. I have acquaintances (ex pats) who live there with their families, and they're quite happy to stay.
Of course it is entirely up to you to decide the level of risk you are willing to accept, so think about it carefully. about 7 years ago