Tokyo and Osaka
 

I am arriving in Narita Tokyo at 4 pm on 9/25 and traveling directly to Osaka to spend a week. Then traveling back to Tokyo for a week. I need suggestions on getting to Osaka from Tokyo. Train or plane? Also, want suggestions on sites to see when in both.

Train is the best way to go. It is cheaper and faster. Look into getting the Japan Rail pass.
Go here and you can find good info and links:
www.japantravel.jopin.com
www.city.osaka.jp/english/

For a JR Pass to be useful you would have to return to Tokyo on October 1.

I'd consider flying to Osaka since you will already be at the airport. If you are flying JAL or American then you can get a Japan visitor's fare for something like 10,000 yen. Then see if there is an airport bus that goes to your hotel.

The price and time could be about the same. Flying requires much less mental effort but taking the shinkansen would certainly be more fun if you are up for it.

I would go to Osaka castle and to Spa World in/near Osaka.

Actually, getting a flight into Osaka Kansai airport would also allow me to visit another Osaka site that I want to visit - the airport itself.

Hi

We took the train when traveling around Japan as we had a one week rail pass. Here is my Japan trip report with pictures http://gardkarlsen.com/japan_tokyo.htm . Maybe you can find some useful info there :-)

Regards
Gard
http://gardkarlsen.com - trip reports and pictures

Probably too late now as you've bought your plane ticket, but the best and cheapest way is to fly open jaw - into Kansai and out of Narita. You can do this with any airlines flying into both airports, and usually it costs little extra over a simple R/T into and out of Narita.
Flying into Kansai from Narita will be the easiest, quickest and most hassle-free. There are a handful of flights daily, but they tend to book up early so reserve your seat now. Even if you don't qualify for Japan airpass or it isn't feasible, you can get a one-way fare for around 10,000 to 12,000 yen by booking in advance. Look at JAL and All Nippon sites.
Getting a railpass and using it for trips to and from Osaka (plus side trips) may work out cheaper, but it depends on your itinerary. You can get a one-way Shinkansen ticket from Shin Osaka to Tokyo for around 13-14,000 yen, and you can ride the fastest and most frequent Nozomi by not using a pass.

Thanks for the suggestions. I have decided to fly JAL from Narita to Osaka on 9/25 and back to Haneda Tokyo on 10/1. I will have about 1 week in Osaka and Tokyo and want suggestions of things to do, mostly on my own.
Thanks for the help.

I think OP should fly NRT to Osaka Itami (ITM), which is centrally located instead of flying into KIX. There are 5:55pm on ANA and 6:35pm on JAL.

From Osaka to Tokyo, OP can get a one-way bullet train ticket (there are no penalties for travelling one way). Rail Pass would work only if OP plans to do more long-distance travelling with bullet trains/express trains.