Technically I think the Crown Plaza is the closest to a major train stations. The hotel is right next to Ikebukuro station. Walk across the street you're there. When you arrive you take the Yamanote from Tokyo Station to Ikebukuro. What's cool about Ikebukuro is it has a direct NEX connection to NRT. What's not cool is that it's limited service. You've have to take a 6:45AM train that would get to NRT a bit after 8AM.

You could bypass the NEX for any of the hotels if the time tables don't match up. I'd be extremely cautious about trying to take luggage on a non-reserve trains during peek times however. Trains are extremely crowed in the morning. You could take the Yamanote or similar line to Tokyo Station and connect to the NEX, IF and ONLY IF you had no luggage.

I'd second patchmonkey's suggestion. Take a look at the limo bus schedule and pick the hotel with the time table that best suites your needs. Unless you're in Japan with a JR Railpass the price between train and limo bus is pretty close.

If you are still considering the train, you can get reserved seats several days in advance. I highly recommend buying them in advance if you're on a tight time line. You can go to a travel office (JR or most Travel Agencies). I did that for my departure on my last visit. I had seats reserved all the way from Kyoto to NRT. It was like clockwork. If you get them at the travel agency all you have to do is tell them where you are, and what flight you're leaving on. They'll fill in the rest.