Simple Mail Transfer Protocol (SMTP) sends mesages; it communicates over several ports (25 & 587 being common). It is not uncommon for these ports to be blocked if you are using a public internet connection, like at a cafe or from a hotel's public wireless network.
If the email account you are trying to send from is a webmail account, like gmail or yahoo, you can simply use the webmail interface as opposed to using Mac's mail client (mail.app).
It's more likely that you are trying to send from a work email. If this is the case, your work should be providing you with some means to connect to the internet other than using public wi-fi, for example a Virtual Private Network (VPN), or small 4G modem.
In any event, sending mail from a non-public network should solve your problem. Most smart phones can be used as mobile hotspots - often free of charge. Often times the app comes pre-installed.
As noted above it is more then likely the hotel internet service provider is blocking port 25 except for people sending emails through their own smtp network, in other words sending email from their domain like att.net.
Check your smtp settings and if it is set to send email on port 25 contact your home isp (internet service provider) and see if they have a alternate port you can use to send mail from. Usually that is either 587 or 465 but also could be port 26. It all depends if they have another port setup for just this type of thing.