Most ISPs will only allow you to send mail when you are connected to their
network, unless you authenticate over SMTP, or connect via POP first. Contact
your ISP and tell them 'I'd like to be able to send email while travelling.
How do I have to configure Outlook to allow me to send?'
f.h.
Microsoft
The response above is confusing and fundamentally wrong. When one is in a hotel, one is using the hotel's ISP. In addition, many if not most people rarely use the email address their ISP provides. I can't remember the last time I saw an email from someone using @verizon.net or similar unless it is spam or an employee of that company. Going further, I don't know of any (read this as vastly fewer than 'most') ISP that actually requires someone to be connected to their network to use an email account. While it is true that to prevent hijacking, email servers are often set up to require SMTP authentication. This is strictly a negotiation between the client computer and the email server itself. One must set this authentication to use email at all regardless of physical location. In fact, without SMTP authentication not only would a user not be able to send email but would be equally unable to receive email.
Peope who experience this problem at a hotel will have it no matter where their account is hosted.
One possible explanation for the "hotel send mail problem" is that the local server at the hotel is setup to reject outgoing email. When the hotel attempts to charge you for high-speed service, bring this up. I'd refuse the charges if they didn't make this policy clear when you requested service. But first check the agreement to ensure this limitation isn't already stipulated.
One remedy is to use webmail access to your email account in these situations. Alternatively setup an account with any of the many free webmail hosts. Some of the latter actually will integrate with your Outlook client so that pieces of your correspondence will not be scattered all over different 'sent mail' boxes.