NEVER connect mains power directly to a project, always use a proper power supply. Typical stepdown modules as you can find on Amazon or e-bay will anyway go up in smoke if you would try this (and cause death and destruction in the process). Mains power if misused is very dangerous.
Power supplies are really easy to get - there may be some in your spare parts drawer, your local thrift store may have some, your local supermarket definitely has them: any USB or old style mobile phone charger that produces 5V regulated power (see the markings on the device; check with your multimeter to confirm both voltage and polarity) is an excellent choice for powering an Arduino project. Connect to either the USB socket or the 5V pin, not the Vin which needs 7V or more.
Other than that, if you can find a 7-12V DC (not AC) power supply you can use that. Connect to the Vin instead. Again those are generally quite easy to find, as there are so many devices that have an external power supply.