Staying in Hutong area in Beijing. Where is best place to go see the Great Wall?

Well, I suggest you visit Mutianyu section. From your hotel, u can take a taxi to Dongzhimen, near which you can find bus no. 867 to take to the wall directly. However, I have to remind you that bus no. 867 is only available during the high season (usually from late March to November 15th).

If you wanna visit Badaling section, it also can be fine. Walk from your hotel to Nanluoguxiang Subway Station to take metro line 6 to transfer to line 4 at Ping'anli Station to get off at Xizhimen. Then walk to Beijing North Train Station to take a train to Badaling.