In addition to Mike's good suggestions, I'd like to add that there are a lot of WiFi devices that support a WiFi "Client Mode: Gives wired-only devices access to an existing Wi-Fi networks". Most, if not all, TP-Link travel routers support that and have the benefit of being physically small. However, those small-sized routers have poor WiFi from personal experience.
If your main router supports dual band 5GHz / 2.4GHz, consider getting a WiFi client to Ethernet device that supports dual band 5GHz / 2.4GHz too.