Thanks.

I also heard you have to re-register after visiting another province/city. If you have registered there, then you must re-register when you come back. Anyone had to do this?

Be sure when you come back and stay in some small city if the hotel you live really make registration for you. I have bad experience with registration in Mengla when go back from Laos. In police they told me I can not make registration myself but boss of the hotel must come to police. But the hotel laoban not do it and when I return to Kunming, they was suprissed in local police when I do new registration why I am not 6 days registred. I not pay nothing but they call to somewhere and look not so happy.... But I not do nothing wrong...

When you stay overnight at a hotel that is the responsibility of the hotel to do the registration.

Yes, you need to re-gister every new entry-stamp when you come back. Means you need to go re-register and get the white 1/2 A4 from the police station.
If you don't do this the visa officer may deny your application to renew or get a new visa. (I was explicitely aked for my latest entry stamp and police record last week).

Ok... since most pf the forum responses about Visa's are years old... (allow me to ask) I have a multiple entry tourist visa and expect I'll want to stay longer than the original 60 days... What does it take to get to stay longer... fly out and come back... Go to the Public Security Bureau and they'll re-stamp it... do I need to pay the Visa fee or ??? Ray

Yeah just leave China and come back. If your renting, make sure to register your residence again, even if you're living in the same place. And day 1 of 60 starts the day you entered, even if it's 11:59pm, that one minute would count as a day.

Multiple entry visa has two parameters (there are more, but two are relevant to this):

1. The overall validity of the visa, for example 1 or 2 or 10 years. I don't know if multiple entry tourist visa has some minimum validity by default, but I'm guessing that such can also be just 60 or even 30 days. You cannot escape this by other means than applying for new visa, or renewing the visa at Entry & Exit Bureau (which for tourist visa can be done only once without leaving the country).

2. The maximum duration per each stay (during the overal validity of the visa). This specific parameter can be reset by temporarily leaving the country (or to a SAR such as HK), even if just to cross the border and coming straight back (though I have heard RUMOURS that this short trick is sometime, somewhere, not accepted).

Since we cannot tell to which of these parameters you refer by your "original 60 days", you may receive inaccurate information for your specific situation.

Public Security may at its sole discretion, extend your visa up to a rumored 2x, obviating the exit/entry stamp requirement. But you should apply early enough to avoid overstaying your visa AND you'll need a valid reason for extending your stay - such as not enough time to visit all the tourist sites you wanted to visit, before leaving China.