How much money to calculate?

Hello there,

I have a stop over at Beijing on my way to the Philippines which is about 13 hours each way. So I wanted to explore the city a bit. Thought about going to the Forbidden City on one way and the botanical gardens on the other. How much money should I change? I will have to calculate for taxi fare (not sure if I can manage the public transport), entry for the attraction and food for both days.

Can you roughly tell how much I should take with me?

Thank you very much in advance.
Kati