I admit I'm ignorance on this.

Is there no country that where an advertising site could establish itself that is outside of the meaningful reach of the U.S. government?

I have a VPN account, and have been trying to figure out TOR. Are there new advertising venues establishing themselves via that server?

You are Commiting a felony by using those sites for prostitution.

Like I said before, you can view porn in the US that will get you 5 years in a federal institution and it does not matter if its legal in the country that the server is located because it is highly illegal in the US.

Took care of trying to establish from off shore servers. Between these 3 pieces of legislature, it basically makes advertising for escort services within U.S. borders illegal, and gives the U.S. government the reach to go after it....no matter what corner of the world it's originating from.

I wish everyone would start to understand this.
I’ve seen many posts on twitter where US women have just hosted their sites off shore thinking they are safely out of the reach of the law. It’s a bit frightening really...

Yes, the Cloud Act doesn't protect Americans who maintain their data offshore.

However, I'm not seeing anything in that Act that would allow the U.S. government to do anything to a web host that is entirely outside the U.S. - at least not without the cooperation of the local government.

An uncooperative local government would likely tell the U.S., "You don't like the website in our country? Block it - like we do with  yours."

It may also be difficult for them to prove who posted the materials that may appear on that site.

I'm not seeing anything in the new bills that would make reading provider advertising/review websites illegal.

I guess they could do that, as you point out they have done with certain types of pornography, but I don't see where they're doing that.

As I see it, there are two issues and they are very different: individuals vs companies.
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If a consenting adult wants to advertise escort services, that is free speech and was usually not investigated or prosecuted by LE until it was in flagrante delicto (caught in the act, with plenty of evidence).  Even now, FOSTA SESTA is not targeting an individual who wants to post such an ad.
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If a consenting adult wants to READ such ads, that is their right and there is nobody going after them. There have been laws about accessing and distributing child porn for many years. Child porn and trafficking are the major targets of all of these laws.  
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FOSTA SESTA is targeting the companies and websites that ALLOW posts relating to the promotion of prostitution, trafficking, child porn, etc.. To protect themselves, the companies (TER, et al.) are no longer accepting ads from consenting adults or anyone else in the US.  
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Support groups have successfully rescued children from exploitation by scanning ads on sites such as bea pee. I don't know the ratio of ads from consenting adults vs child trafficking on beepy. Anyone want to take a guess? Less that 1%? Less than 0.5%? Whatever ... the support groups were against FOSTA SESTA as it will now make it harder for them to find the children.  
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The only way to post ads on the internet is to "inject" them there. The only way to do that is via a company (beepie, etc., TER) and, ultimately, via an ISP (Verizon, ATT, Comcast, ...). The law is targeting the big companies and ISPs with the threat that: "If you post an ad promoting any of this stuff, we are going after YOU, not the lone person placing the ad."  Hence, it is harder and harder for an individual to find a way to place an ad on the internet.  
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Even if an individual was savvy enough to bypass TER, bea pea, etc., by setting up their own tiny company, to set up a server in their basement or living room, and to connect to the internet via a local ISP (Verizon, etc.), the ISP could still shut them off the minute they determined that is was a company using them (Verizon) to post even ONE ad offering Escort services that LE would interpret as the promotion of prostitution.  LE can't go after a lone Provider sitting in her kitchen making sandwiches for her kids. LE can only arrest a Provider "in the act." However, LE can now go after the companies that facilitate prostitution by allowing an individual to post an escort ad.  
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That's my take on this. Keep the individuals (Providers, clients) and companies (TER, bee pea, Er*s, etc.) separate in your analyses and critiques.  Harming the business of consenting adult Providers is the "collateral damage" of these laws.

Obviously USA laws are not binding on other countries.  The US is limited to blocking foreign websites (with court orders to entry point communications carriers) or pressuring foreign governments.

VPN and TOR easily get around blocked IP addresses. TER isn't a case of the gov blocking them, they are self blocking IP addresses arriving from the USA.

The immediate future should see a lot of offshore "dating" sites pop up.   Either out in the open or behind self-blocking like TER.  There is money to be made and plenty of greedy people in the world ready to try and cash in.

So we should see things return to a new state of commerce with a lot of offshore sites and a lot of VPN/TOR education among clients and providers.

Long term the gov could go after VPN's and TOR routers.  I suspect that would generate a lot more outrage in the Internet community.   Could happen, but I don't expect it to happen quickly.