Be a Cautious "Road Warrior"
First, as mentioned earlier, never sign in to any account on a shared computer in a hotel lobby.
Second, realize that hotel networks, wireless or wired, are entirely insecure. Yes, there is an illusion of security as you have to enter a password or PIN for the router to forward your packets.
But this is just a "captive portal" system. It makes the hotel's liability lawyers happy and it increases revenue if you have to pay for the access. There is absolutely no security for the user in a hotel network. Anyone else in the hotel could be capturing all your data, including passwords and data content.
Only use a hotel network for entirely non-critical traffic (browsing random websites) or for communication encrypted end-to-end through a carefully configured TLS connection or SSH, or through a corporate VPN (that is, a Virtual Private Network).
Travel provides more chances of losing your electronic devices. See the next section for how to encrypt data stored on phones, tablets, and laptops.
A mobile hotspot may be worthwhile. Yes, mobile phone networks can be hacked, but they're far safer than hotel networks.
Advanced topic: see how a $25 per night hostel has far better network security than a business hotel costing at least ten times as much.
Even more advanced topic: you could carry an entire virtualized computer on a USB stick.
Next: Encrypting mobile devices ❯