Gaming console. It is very easy to pair an old Android device with the television via Google Chromecast and an HDMI cable. You can download a selection of emulators for your classic gaming consoles. There are apps from Super Nintendo to Sega Genesis available for Android. You can pair a Bluetooth gaming console with your Android device and you are good to go. PlayStation remote controller works really well with Android devices.
Gym device. Your old Android device can be an ideal gym tool. You can format it, remove unnecessary apps and data. This avoids unnecessary distractions in the gym. You can use your device as an MP3 player while you sweat it out. You can pair it with a cheap fitness tracker or smartwatch for extra functionality.
Desktop computer. Yes, you can install your old Android device as a desktop computer. Even the oldest smartphone is more powerful than old desktop computers. You can install Debian or any version of Linux operating system on your device and connect it to a monitor. Then, sync it with a Bluetooth keyboard and mouse, and you are good to go.
Car GPS and music player. There is no doubt that you can use old Android device as a GPS navigation unit with your car. There are a number of great navigation apps available for Android (Google Maps, CityMapper, Waze and others). This gives you the option of using the old Android device as a dedicated GPS unit in your car. You can plug it in using an auxilliary cable and double up the usage as a dedicated stereo/MP3 player.
Wi-Fi extender. If you have weak Wi-Fi signals in your house or office, you can extend the signal range using your old Android device. You would need to install apps like fqrouter2. The app will pick up signals and repeat it. However, the app requires a rooted Android device.