I agree with ads-ee, it's recommended to add a secondary decoupling cap to the ADXL345.
Further remarks:
- Make the UART pins (30 and 31) external on 4 pin header together with VCC 3.3V and GND. Having a communications port aside from ICSP is always useful for debugging.
- Add a filter before the buzzer and drive it with a PWM signal instead of a square wave to remove the high pitch noise and make the sound more "natural". Ideally, choose an active filter with a rail-to-rail opamp like the MCP601 to avoid sourcing the drive current for the buzzer with the MCU.