I often travel for business and use hotel wifi. I have installed Little Snitch and VPN-Outline for internet security. Should I buy a mini router? Will it keep my computer safer？ Otherwise，with or without a router, there is any difference in internet security. In other words, a simple router will help in which ways?
A small router would help isolate your device from the hotel network, relatedly it would reduce your wireless exposure, assuming you turn Wi-Fi off on your computer as you are using the router.
You may conflict with the hotel network if you misconfigure the router, this may cause them to dislike you and possibly, disconnect your networking.
You may also find that ensuring your computer firewall is properly configured is as effective and less hassle, than carrying a router and peripherals.
Depending on what you try to protect against, a firewall might not be sufficient. It (might) secure you from attacks directed at your machine directly from the hotels network. That actually is something to think about because people in hotels tend to have boring evenings where they might have funny ideas or bring a lot of malware (unknowingly).
Anyways. One of the more present attack scenarios in hotels are man in the middle attacks. Attackers on the same network still tend to utilize attacks such as arp-spoofing or attacking the hotels infrastructure (such as routers or switches). The main goal of a lot of this is: eavesdropping. If your Browser/OS/App/whatever program is configured or programmed badly you might have unencrypted communication channels or encrypted ones that are interceptable (by downgrade to unencrypted communications). One option to protect against those attacks is a propery configured VPN that encrypts all your communication until a single defined endpoint "sets them free" to the internet.
Tl;DR: A better combination than firewall + router would be: firewall + vpn.