Where are IP addresses stored on Android? Where are IP addresses stored on and Android device? In what location on disk, or otherwise; how are they stored?
Under Settings, Wi-Fi, , Modify Network, Advanced Options, IP Settings, you should have a choice of Static or DHCP.  Choosing Static adds input boxes for IP address, Gateway, Network prefix, and DNS.

If you don't have this, I suggest trying a third-party app such as WiFi Manager.

Finally, if you're really talking about where in the filesystem this is stored, it's in /data/misc/wifi/ipconfig.txt, and is managed by the WifiConfigStore class. This is not a public API and is only used from class WifiStateMachine.  However, you can find out the format of this file by viewing the source: WifiConfigStore.java.