This depends on the type of screen you want to interface. An Arduino UNO can with big effort interface a VGA signal with very low resolution and only few colors. Better are little screens (like small OLED screens or small LCD displays with integrated controller). Using a more capable Arduino (like the Mega) can extent the capabilities of your project. The RaspberryPi has of course big display capabilities (like 1080p over HDMI).
There is also another side to the problem: A self balancing robot needs to control its motors very fast (changing the direction fastly depending in sensor input). A RaspberryPi is in principle a computer, not a microcontroller. Programs in it don't have a garanteed time of execution, so especially under high load the program might have to wait for its turn, effectively destabilizing the robot. For these real time fast applications a simple microcontroller is fitted better.
Since you also want wireless control you might be interested in using an ESP (WLAN) as a microcontroller.
All in all you should use a microcontroller for driving the balancing logic and motor control. Depending in your needs you can either use only this microcontroller to do all the other things too or connect another board as a master (eg over I2C vor SPI) which tells the microcontroller what to do. For this a raspberryPi is good.
If you provide more information about the concrete target capabilities you might get a better answer. The scope of your project is too open for clear answers.