How to find your router's local IP address using an Android device

Find and open Settings on your device.

Tap on Wi-Fi

Long-tap on the active Wi-Fi connection. (Long-tap reaquires a tap and hold for about two seconds)
Choose the option Modify network config.

Check the option Show advanced options.

Scroll through the list of options until you find the filed Gateway
This Gateway field displays IP address used by your router for the local network.
Write down the IP address which you see displayed in the Gateway field.

Tap Cancel to close.