They usually have an interface so that when you get to a hotel, you can either plug them into the hardline or they will let you connect and then select the hotel's wifi and enter the password.
The great thing is that all your devices will already have your travel router wifi info saved. So when I go to a hotel and fire it up and connect, all our phones, ipads, Roku, even an Amazon echo we sometimes take will will all connect right up.
Sometimes I even luck out and the lan cable going into the TV will be unmetered. One hotel I was getting 100mbps up/down all week for free.
Or you can buy an older used router for ~$10 that supports FreshTomato or DDWRT, I know those support simultaneous AP and client mode. I spent a year using one for such needs and worked well on an E2500. Or buy a dedicated like OP said as it's probably less trouble and more reliable, depending on model.
In a pinch you can just spoof the wifi MAC address of the chromecast/firestick/roku with a PC, connect to the wifi, deal with the captive portal, then connect the actual device (change your MAC back unless you want fireworks).