Xiangshan Park, Beijing

Yes, you can still see the red foliage of the trees at that time and it shall be the best timing to enjoy that. From this hotel, you can walk to Chongwenmen metro station to take subway line 2 to Fuchengmen. Leave from exit B to walk to Fuchengmen Inner stop to take bus no. 714 to the hill. The fare for metro + bus is CNY4 and the whole trip takes around 1.5h.

I remember there are several trees with red leaves in the north slop of Summer Palace. During your travel time, you will see the foliage. But it is not as fascinating as that on Xiangshan.

Your hotel is around 2 miles to the Forbidden City. You can take a taxi there at the cost of CNY13-15. It takes around 10 minutes to arrive.

Thanks for your advice ! What is your opinion, how it is better to plan the journey, from the point of view of transportation ? First visit at Xiangshan Park after that at Botanical Garden, or first visit at Botanical Garden after that at the park? My impression is, first the the park, but someone who made these visits know better !

A faster route is take subway to Zoo Station, come out Exit D or C3, walk to Bus Station to take Bus 360 (express) to Xiangshan Park (bus journey is about an hour n 10 mins).

Your gut feeling is right: Fragrance Hill 1st, then Botanical garden (rather flat land with monuments n lakes). 2 places will take you more than 5-6 hrs of walking. Have some bottled water, snacks or just eat there.

A faster route is to take Bus 360 (Express) from Subway Zoo Station, Exit D or C3. Slight more than an hour bus ride. The challenge is many passengers at the Bus Station, so you may have to wait for next bus. Every 10 minutes.