Am I allowed to travel all cities in China? Are there any limitations?

If you are American, no limitations - but in some towns, you may have to register stating that you are staying there for the night.

If you are following a tourist group, stick to the group and you will face no problems.

If you are traveling alone, with a companion or not in a group, the authorities have a right to question your coming ins and going whereabouts.

Detention is possible if they felt that there is a violation of your visa.

I have been traveling in and out and no problem so far.

How the do we know? Where do you come from? If you come from China, the answer is yes, everywhere except Tibet!

for some special cities - like Zhuhai, Shenzhen - but you just show your passport - it will be fine

For HongKong and Macau - u need a local permit

remember to go to Tibet - worthy going really

ENJOY

There is a number of so called "closed areas", that you are not allowed to travel to on a normal tourist visa. For some you can obtain an "Alien Travel Permit" but some are downright off-limits for foreigners. You won't get a permit for these and get into trouble if you're caught there.
But nearly all places of any interest for a tourist are free to go with the notable exception Tibet.
The regulations about the permit you need for Tibet are changing frequently, but expect that you need a travel permit for Tibet and that there are only three legal ways to go there: fly into Lhasa, or overland from Golmud or Kathmandu. All other routes, especially the one down from Kashgar are closed areas.
I travelled a lot in China and the only other time I had to obtain an Alien Travel Permit was to get to a village on the Amur river right on the Russian border, so unless you plan to go to Tibet it's quite unlikely that you'll face problems with closed areas.

as a US citizen you can basically travel to most places. in shenzhen i came across one road that only chinese nationals with valid ID cards could go on.