The park was built in the Jin Dynasty (1186). The park is open all year around but the best time to visit it is in autumn, when all the leaves turn red/orange colour and it will just leave you mesmerized.
Beijing Zhíwùyuán (Beijing Botanical Gardens), are located next to the foot of Xiangshan. It's a world away from the hustle and bustle of the city centre, and would be ideal for anyone who wants to while away their time in beautiful surroundings, including the greenhouse and a special rose garden that contains at least five types of rose flower. Quite romantic too!
After spending the day at Xiangshan Gongyuán and Beijing Zhíwùyuán, it would provide a nice ending to the day if you visited the town of Wu Dao Kou - an area near the Tsinghua and Beijing Universities, popular with tourists, foreign students and expats alike. There are a myriad of restaurants of all different types of cuisines (including Indian, Italian and Mexican). There are also some nice Japanese and Korean restaurants where you can drink authentic Japanese or Korean beer over a nice meal.
I would recommend that you set aside a whole day to explore both Xiangshan Gongyuán and Beijing Zhíwùyuán (including travelling to/from the city centre, which takes about 30 minutes by taxi, costs approx 50 RMB from Beijing city centre). It takes an hour by the many buses that run between the city centre and Xiangshan, if you are adventurous, but costs only 6RMB one way. Wu Dao Kou is located within 30 minutes of the city centre, and has a metro station (on line 13 from Xizhimen) and is easy to get from the botanical gardens by taxi (about 20 minutes and costs approx 30-40RMB).
All taxi drivers will understand you when you mention the names of the places, as they are written above.