www.happycow.net good info for you

Veggie not a big problem at all rice is the base food.

Indian restaurants abound in towns cities...

Well, I personally remember only a few unmistakably vegetarian meals - tung choi or eggplant fried on garlic and soy sauce or corn soup, potato pancakes, etc. Not sure about the eggs in it, though. From time to time I came across strictly vegetarian restaurant most usually connected with monastery, or run by Buddhist monks/nuns, I believe I saw some list in Lonely Planet or Rough Guide.
Nevertheless, my vegetarian friends travelled to China and got them written a message in Chinese beforehand - just something like "vegetarian food", "no meat", etc. and if they couldn't pick anything from the English menu, they showed the message and it always worked out somehow.

There are plenty of vegetarian choices in China/HK.

For breakfast, look for rice porridge, soy milk, onion pancakes. Just stay away from noodles which may have eggs in it (Rice noodles would be okay.) Yogurt is available too.

If you do dim sum in HK, there are lots of vegetable options as well.

For lunch or dinner, there are usually all kind of stir fired vegetable dishes on the menu, plus tofu, mushrooms, etc., plus rice of course.

In the big cities, there are also usually vegetarian restaurants in town that can get really creative with their vegetarian dishes.

我 是 吃 素 的 Means I'm a vegetarian.

Just a thought about your itinerary. I suggest you to go see one water town in the Shanghai/Hangzhou area. We did Xitang the last time we were there and loved it. It is located between Shanghai and Hangzhou and can easily be done as a day trip from either. You can check out our report on that if interested.

http://www.TwoCountriesAYear.com/side-trip-from-shanghai-xitang/

There is lots of yogurt in China, but all is sweetened. So be prepared as you will not find the same sort of yogurt Indians eat with their meals.

Cheese is available but not too popular as Chinese are still getting used to the taste.

But vegetarian dishes are not too hard to find. You will have to ask your hotel personnel to write down on a piece of paper you want only food with vegetables and beans and no meat and eggs. Truthfully it can be hard sometimes as they use some sort of little meat to flavor even vegetarian dishes.

But you can find some good dishes of eggplant,potatoes onion pancakes like a paratha, rice with vegetables and also plain rice.

There are very good sweet yogurts with fruit. There are lots of varieties of fruits and thus you can manage easily.

Of course, you can find Indian restaurants in all large cities.
Good luck and happy travels.

It may be good idea for you to carry some small snacks so you can munch while hunting for a good place to eat.

The problem with eating in restaurants that serve meat, as you know, they often include meat broth in sauces so vegetables aren't necessarily vegetarian. But there's a tradition of entirely vegetarian restaurants in China. In a place that calls itself "vegetarian" the menu will have what appears to be all sorts of meat dishes and it can be momentarily confusing. However the "meat" is actually tofu made to mimic meat and it can be quite entertaining once one is used to the idea. So just ask where you stay to be directed to restaurants that are entirely vegetarian.