Hit the streets and some people will approach you in no time looking for private tuition, very few foreigners actually "hang out" or explore their city in China, most go from point A to point B as fast as possible.

Walk into the fancy new malls in downtown areas most have a training center's branch.

Note that it's illegal to work on a student visa, if you are caught you can be fined and imprisoned while waiting for your deportation (at your own expense) and blacklisted from returning to China for 5 years, but then again this is China so chances that this will happen are almost non-existent.

Why even bother to offer advice to to some moron posting Anon requesting assistance from him to do something illegal. He probably has no business teaching English.  If you are sooo incompetent that you can't walk around a big city like Hangzhou and look around then you deserve no assistance.  Finding schools, private students , is sooo damn easy. What is the purpose of this post?

Sure. Next time I'm in Hangzhou, I'll make inquiries on your behalf.

Check out the jobs section here and on the Hangzhouexpat website 

OH SURE please come work at my school in Hangzhou. We are a high end school that hires people on student and tourist visas. Based on the information you provided in the OP I'm sure you'd be a great fit. Please send me a picture at 43833335343@126.com and come to our school at the intersection of datroll lu and fuckoff jie.