Need creative ideas for "inspiration" on fun project

You didn’t state which FPGA, but assuming you grab an older classic one that can support 5V outputs, you can then grab a piezo buzzer from an old smoke alarm and have the FPGA drive it directly with steady state voltage. Or you can grab a musical buzzer from one of those fancy hallmark cards and drive it with the FPGA too :D

Another option is grab a small speaker and build an oscillator inside the chip to the frequency of your choice. Then select the I/O standard and appropriate power supply that will produce a volume level of what you desire.

BTW, it's illegal to remove existing smoke alarms from a building.