Something like this would work well. What you need is an access point, not a router.
You could make a standard home router work just like an access point though, just turn off the DHCP on the router so the that you don't mess up the network you are connecting to. Then instead of plugging the ethernet cable into the WAN port, plug it into any of the LAN ports, this bypasses part of the router, giving you access to a wired LAN from wifi.
I have one of these... I configure it to have open WiFi with “mac filtering” whitelist turned on (only allows my DSi to connect and nobody else) and I only have it powered on when I need it.
TP-Link N300 Wireless Portable Nano Travel Router (https://www.amazon.com/dp/B00TQEX8BO)
I have it plugged into the back of my primary router via network cable. It’s Nice. Small. And easy to use.
TP-Link nano is what I have. Only used it two or three times in a year, but works fine. Also used it when my home router took a dump.