Nowadays, most of the modern routers are creatively designed so you can leave them on all the time. Hence, there's no harm if you keep your router on all day long or all night. But, note that, if you leave your router on all the time, you will have to reboot it regularly to prevent issues in internet connectivity. Further, many offices, establishments and businesses especially with open Wi-Fi hotspots turn off their routers when they close at night. They prefer doing this since it won't be used for 10 to 12 hours or even more. Additionally, this conserves power and increases the level of security.