Imperial Garden (Yuhuayuan)
At each of the four corners of the garden there is a pavilion. These symbolise the four seasons. The Pavilion of Myriad Springs (Wanchunting) is the most famous and occupies the eastern corner. Built in 1535 and restored during the Qing dynasty, as its name implies, it is this pavilion that symbolizes spring.
Located in the north-east is Duixiushan, Gathering Beauty Hill is a little artificial mountain with a cave. Yujingyuan (Pavilion of Imperial View) sits on top of the mountain. Emperors would climb up to the pavilion on the Double Ninth Festival to enjoy the scenery with the royal family.
At the northern end of the garden is Shenwumen, the Gate of Divine Might and the rear exit from the Forbidden City.
Having visited all the sites on the east and west sides of the Inner Court, you may leave via the Gate of Divine Might.
Go north to the Hall of Imperial Peace (Qin'andian), Gate of Divine Prowess (Shenwumen). See introduction to the Moat, Corner Towers of the Forbidden City (Jiaolou)
One can also see the Six Western Palaces (Xiliugong) to the southwest, or the Six Eastern Palaces (Dongliugong) to the southeast.
Further Reading: How to visit the Forbidden City
April to October: 8:30-17:00 (last entry 16:10)
November to the next March: 8:30-16:30 (last entry 15:40)
So of course visiting whenever you want is impossible.
If yes, after you take the Exit, you should walk westwards for 220 yards, take the bus No. 109, 101 or 58 from Gugong station to Dongsi LUKOUO East Station. Then walk about 65 yards, you will reach the subway station.
It is about 1.3 miles between these two places, you can also take a taxi to reach, the fare is about CNY15- 20.
For this museum, the visitors can only enter from the Meridian Gate and get out of from the Shenwumen.