Okinawa & Koyasan in January

I'm planning on going to Japan in January, specifically, Koyasan and Okinawa, and was wondering a few things:

1. Is January a good time to visit Okinawa? Not that I'm a beach goer, but will the beaches be open at that time?

2. What is the weather like in Koyasan in January? The best that I can find is average temperatures in Osaka and Wakayama Prefectures. I know it will be cold, but I would like to know if it will be unbearable.

3. I plan to spend 3 nights in Naha, 1 night on Miyako Island, and 3 nights on Ishigaki Island, with a day trip to Taketomi and Iriomote (same day). Is this doable? I would welcome any suggestions to this part of my itinerary.

4. When is the Nago City Cherry Blossom festival?

5. I would like to go to the Toshi-ya Archery Contest at Sanjusangendo in Kyoto. Would I need to buy a ticket? How would I be able to be a spectator.

Thanks for any help you can give.

Is January a good time to visit Okinawa?

Not really. The weather tends to be very cloudy during this time of the year. But temperatures are milder than on the "mainland", especially during the nights. Average daytime temperatures are typically around 15-25 degrees.

Not that I'm a beach goer, but will the beaches be open at that time?

Beaches don't close. Most beaches are accessible throughout the year. Several companies offer diving and snorkeling tours throughout the year (in wetsuits).

What is the weather like in Koyasan in January?

Average daytime high: around 3 degrees
Average nighttime low: around -4 degrees

If you bring appropriate clothes, it will not be unbearable.

with a day trip to Taketomi and Iriomote (same day). Is this doable?

Theoretically, yes. But I recommend to allocate one day to each island.

4. When is the Nago City Cherry Blossom festival?

Late January to early February.

As always, thanks Uji. Any info on the archery tournament? Also, are your temperatures in celsius/centigrade? I meant to specify in my questions.

Because Okinawa tends to be cloudy in January, can I assume that it will likely rain a lot too?

Any info on the archery tournament?

When I don't answer a question, I am afraid, it means that I don't know and cannot find the answer.

Also, are your temperatures in celsius/centigrade?

In Celsius.

Because Okinawa tends to be cloudy in January, can I assume that it will likely rain a lot too?

To give you an idea, below I list the number of days on which there was one or more millimeters of rain during past Januaries:

2007: 12 days
2006: 13 days
2005: 12 days
2004: 12 days
2003: 7 days
2002: 9 days
2001: 11 days