Best bet is probably going to be using something like OpenVPN on port 443 in TCP mode, which basically looks like regular HTTPS. It’s a hotel, I doubt they’re going to be doing deep analysis to detect signs it’s OpenVPN. It’s detectable easily but they wouldn’t spend the money on that advanced of a firewall.
My guess is they went for an allowed list of ports rather than blocked, so it lets DNS (53), HTTP (80), HTTPS (443), probably also POP/IMAP/SMTP (110, 995, 143, 993, 465)