For what type of account? Pop3/IMAP? Contact them and ask which SMTP server
you can use on their network. If they don't provide one you can see if
enabling authentication to your current SMTP solves your issue. You can do
this by going to your account settings and press the More Options button.
You are obviously not on your e-mail provider's domain while at the hotel.
If your e-mail provider is your ISP, you will almost always be off-domain
when travelling. You need to find out what setup is needed, if allowed, by
your e-mail provider to authenticating to their mail servers when you are
coming from someone else's domain. Authenticate to the mail servers. You
may need to use non-standard port numbers, SSL, and other settings. Ask
your e-mail provider for the details.