Trevor,
"Colorful" doesn't necessarily help as many squadrons will paint a special scheme on an aircraft for their show, but on the assumption you are talking about the camouflaged F-15s of the Aggressor flight, the show you want is the open house at Nyutabaru Air Base.
http://www.mod.go.jp/asdf/nyutabaru/
https://www.google.com/maps/@32.0871823 ... 123,15.06z
This year the show is on Sunday the 6th December. The local railway station is called "Hyuga Shintomi", Miyazaki is the nearest local town and civil airport.
If you, with the help of an online translator like Bing Translator, can navigate the Japanese language website, the closest hotel is AZ Shintomi:
http://www.az-hotel.com/shintomi/
Which is about 30 minutes walk up the hill to the eastern end of the runway, and the north facing room overlook the turn from base leg onto finals for runway 28. Which is the runway in use most of the time at that time of the year.
But AZ Shintomi are already fully booked for the show weekend.
There are several hotels on Booking.com or with English language websites near Miyazaki railway station:
http://www.toyoko-inn.com/e_hotel/00101/index.html
But it also looks like many are also already booked up.
I push the railway station as cars tend to be excluded from the immediate area around the base from the Friday afternoon. Parking tends to be off-base with shuttle buses, but the queues for the buses look terrible. It's a very popular show.
The ticket machine at Miyazaki Station has an English language option; a one-way ticket to Hyuga Shintomi costs 370 yen, but you have to put the money in the machine before you can select the destination. If the station isn't manned, take a ticket from the machine by the door as you get on the train, then present it with the fare at the ticket gate if at Miyazaki, or to the driver if getting off at a small station.
http://www.hyperdia.com/
The first train from Miyazaki, at 06:05, will be packed for the 21 minute journey to Hyuga Shintomi, but once there you have the choice of taxi or shuttle bus to the show.
Or not. Miyazaki has a south facing crowd and farmland crossed by numerous tracks along the southern side.
So if the weather is good, and you want to take photographs, and you are prepared to accept the risks associated with standing underneath military jets doing high speed formation aerobatics, your best bet is to walk (or take a taxi as far as you can, to the junction at Cho Shudai, then walk) from the station to the southern side of the base. Which attracts a large assortment of Japanese photographers. Just watch out for the pushbikes.
As well as the Aggressor F-15s, which for the last few years have done a 2-ship display, Nyutabaru has the F-15 conversion unit, 23 Hikotai, which have also been doing 2-ship displays recently, and the F-4EJkai Phantoms of 301 Hikotai, which on the last two shows have done 2-ship strafing runs for their flying display. Plus the Search and Rescue flight, which do a demo with a UH-60J and a U-125A. It is also normal to have a display from a Tsuiki based F-2A, the T-4s of the Blue Impulse team, parachuting from a C-1 transport and possibly a display from a USAF F-16C from Misawa. The based aircraft open the show with a massed flypast, including T-4 trainers from the F-15 and F-4 squadrons.
In the week leading up to the show there are a number of rehearsals, usually with two each from the fast jets, and one from the flypast, the SAR demo and the F-2. Arrivals are mostly on Friday afternoon, with a few late on Saturday and the JMSDF P-3 and SH-60J early in Sunday morning. Saturday is usually a dress rehearsal with most but not all of the flying programme taking to the air.
But as with most weeks at that time of year, expect to lose between a half and one day of the week to weather. If the sun is out it will be very pleasant, but any wind or cloud can turn it cold - warm clothing is recommended.
And that's the main problem with visiting Japan in December - the days are short and the weather can be cold /bad, especially further north. But if you do decide to go, you can head to Okinawa which is further south, hence warmer (but not necessarily dryer) and which is the location for the open house show at Naha Air Base the following Sunday, 13th December. If flight schedules remain the same as the last few years, there is one daily flight from Miyazaki to Naha - ANA Flight 3767 departing at 08:45.
At Naha, rehearsals tend to take place in the civil traffic lull between 08:30 and 09:30, but the aircraft movements at Naha, Futenma and Kadena should be sufficient to keep you occupied for the rest of the time.
I hope this helps,
Jonathan.