For the sake of brevity, I will try not to duplicate the already good advice given in other answers.
Ask yourself what you want. Do you want your old job back? Do you want a promotion to leapfrog your manager? Do you want the manager who accused you fired? What about the HR rep? Do you want your reputation restored among all your colleagues and possible clients/suppliers? And if they take you back because they're too afraid to get sued, don't be afraid to demand some guarantees from them. Now is the time you have the most leverage. Don't accept your job back now, if they're able to fire you six months down the line for some other unrelated reason.
By now I'm assuming that you've provided a copy of the receipt to the CEO, if not, I think you should do that, at least. If you sue the company for defamation, but didn't do what you could with the company to mitigate (and possibly stop) future damages to your reputation, you may be held responsible for those future damages, not your employer's.
However, if you've shared a copy of the exonerating evidence with the CEO, the HR rep, and your former manager, but nothing is done to repair your reputation among your colleagues (assuming they know about the initial accusation), that's going to be on them.
So then, the questions become: Can you prove you gave a copy of that receipt to the CEO at least (should he later deny it)? Can you independently verify what your former colleagues know of the incident (if anything) and should they know something can you verify that they've subsequently received the news about your exonerating evidence as well? Do you know how some of them feel that the same exact thing could have happened to them? Don't answer my questions on here, keep these answers to yourself. I'm also assuming you've signed away your rights to contact your former colleagues. So if you contact anyone to ask those questions, make sure it's someone you trust.
And at this point, if you feel your bridges have been burned, you may want to sue your former employer.
When in doubt, sue everybody. This way, the defendants start pointing fingers at each other (instead of trying to protect the relationships they have with each other).
So I agree with Deepak (in his earlier comment), you should also sue AirBnB. But not because you'd win against AirBnB, but because by suing AirBnB, they'd point their finger squarely at your manager for going outside the safety of the platform for trying to resolve the issue and sending the money directly to a potential scammer.
In addition to that, suing AirBnB would ensure that they'd deactivate the host for the camera (or at least, I hope that's what they would do).
Of course, you should sue your employer for wrongful termination, defamation of character, breaching your privacy (and possibly peeping/sexual harassment/providing an unsafe environment). This last one is because the AirBnB location was a work supplied employee accommodation as far as you're concerned. You didn't choose it. Furthermore, there is a reason many very large employers refuse that their employees even stay at AirBnB locations in the first place (despite the huge cost savings). It's because of the liability. The liability is huge for an employer to have you stay in a stranger's house and then have something happen. And if there was any peeping going on in those premises (whether you're female or male), it's their job to address it and take the issue very seriously (which obviously, they didn't even try to).
You should also sue both your manager personally and sue the host in civil court as well (but if you can get some criminal charges filed against the host for peeping, or taking that picture, that would be a bonus too). When thinking about criminal charges for the host, contact the local DA at the location in question, possibly the State Attorney of that State, and possibly the FBI. If you don't get the initial reaction you're hoping for, emphasize the AirBnB and the peeping angles.
I am not a lawyer, my own advice may be really bad, so take everything I say with a huge grain of salt, but the advice you were given about being an "at will" employee was absolutely awful for sure. That is why some people are asking you in the comments if you mistook the company's lawyer advice for serious objective advice, because none of us can fathom that your own lawyer would have said something like that to you. I understand you're in an "At will" State and the employer can let you go for any reason, but letting you go 2 weeks after a theft allegation makes it anything but an "at will" termination.
And I understand you were pressured to sign that piece of paper to protect your professional reputation (and possibly get some severance pay and unemployment benefits) and there is no shame in that, but now that you know you can easily be pressured into signing documents, don't ever go to your former employer by yourself and don't negotiate with your former employer by yourself. If they have a document they want you to sign, take it with you to show your lawyer (or take it with you back home at least). From now on, don't ever sign anything else under pressure. Don't even enter a room with more than one person when dealing with such a difficult issue. Dealing with a superior is intimidating enough, but dealing with a superior, the CEO, and an HR representative. You were at a huge disadvantage talking to them alone. It would have been better that you hadn't signed that piece of paper, but now that you did, don't assume that the document you signed will necessarily stand up in court either.
Search for a good employment lawyer. This part is easy. Just read any local news story about wrongful termination cases successfully won that involved the wrongful accusation of theft by the terminated employee. And work your way backward. If the name/contact info of the attorney is not listed, contact the journalist who wrote the story and ask him/her for it. And don't be afraid to interview multiple lawyers.
If you can do some research on the host, any manager/employee of the host, any family member of the host, and the landlord of the place. Do that as well. The more facts you have at your fingertips, the less work your lawyer will have to do. Use Google, but don't get scammed by the internet either. County records are free (except for photocopy costs). Don't go through an internet intermediary that costs money. If you're too far from the county in question, ask a local friend to do that search for you, or try a public University with a law library, ask their librarian for help, and/or use their free access to Lexis Nexis.