Cities i plan to visit

Hey everyone, i'm going to Japan for roughly 20 days- 1st Oct to 20 Oct. Going to bombared you with a load of questions so if you could answer any of them that would be much appreciated! =)

Travel plans:

1st- 5th Tokyo. With a day trip to Nikko. Any other places recommend for day trips?

5th-8th Kyoto

8th-10th Osaka. Is there much to do in Osaka?

10th-13th Beppu. Really want to try the different hot springs etc. Does anyone know how long it takes to get to Beppu from Osaka by train?- will have a JR rail pass =)

13th-15th Nagasaki. Would you recommend Nagasaki or is there another city on Kyushu that you think is a must-see?

15th-18th Okinawa. Flying from Fukuoka to Naha. Is the weather in Oct good for swimming, sunbathing?

18th-20th Tokyo. Flying from Naha to Haneda. Not sure what to do for the last two days!

So yeah, any help on these would be awesome!

Any other places recommend for day trips?

Depends on what you are interested in. Here are some suggestions:
http://www.japan-guide.com/list/e1103.html

8th-10th Osaka. Is there much to do in Osaka?

Yes! Here are some of the main attractions:
http://www.japan-guide.com/e/e2157.html

Does anyone know how long it takes to get to Beppu from Osaka by train?

It is explained below:
http://www.japan-guide.com/e/e4705.html?aFROM=2157_4700

13th-15th Nagasaki. Would you recommend Nagasaki or is there another city on Kyushu that you think is a must-see?

Nagasaki is Kyushu's most interesting city, in my opinion.

15th-18th Okinawa. Flying from Fukuoka to Naha. Is the weather in Oct good for swimming, sunbathing?

Yes, October is one of the best times of the year for visiting Okinawa. And it is warm enough for swimming and the beach.

I would suggest travelling to Kagoshima from Nagasaki and fly to Naha from there. Kagoshima is also an interesting city and totally different to Nagasaki.