Akasaka State Guest House

Akasaka State Guest House, or Akasaka Geihinkan (赤坂迎賓館), is one of the two national guesthouses in Japan, the other being in Kyoto.
It was built in 1909 as the palace for the then crown prince later to be Emperor Taisho. It became a detached palace of the emperor when he was enthroned, and after WWII it became a property of the government. Ever since 1974, it is used as a guesthouse for visiting state dignitaries.
This former palace is a complete Neo-baroque style building designed by a Japanese architect and is designated as a National Treasure of Japan.
It's a 4-minute walk from Yotsuya Station of the JR Chuo Line, Tokyo Metro Marunouchi Line or Namboku Line.
The public opening of the guest house has been widened significantly since April 2016 (see below).

Since the April of 2016, the public opening days of this site have significantly been expanded.
You can see the garden and the exterior of the building from 10am to 5pm without reservation for 300yen, though you have to go through a security check.
If you want to see the interior of the main building, you need to either make a reservation or line up on the day you visit. The admission is 1,500 yen.
If you want to see its traditional-style annex additionally, you must make a reservation beforehand. The admission is 2,000 yen.
For details, see their official English website shown below.