Sheri, I am of no help with Osaka recommendations; seems like Masaki is giving you excellent advice. I would recommend, however, posting questions on the FlyerTalk Japan Forum here .

They would be able to give advice on both the transfer NRT to HND and also on transportation and hotels in Osaka. I tend to agree with the recommendation of staying at the airport hotel as you will be dead tired after that trip.

edited to add:

I see that you have already found the Japan board on flyertalk. Now that you have your HND flight, I would ask again about hotel options in Osaka.