Send a (push) message to everyone who is in the range of my Wi-Fi router?
The only way I can think of doing this over wi-fi is if you have a captive portal, where the users have to accept a TOS each day for example - you could then amend the portal page to include your daily message. There are some open source options available but you'll likely need to purchase a dedicated router/hotspot.

Another option would be to use Bluetooth/iBeacons - a lot of people leave it switched on so they can easily connect with speakers/car kits etc, and there's a lot of options available - a quick Google for "Bluetooth push advertising" or "iBeacon" should help. It's possible to set the low cost RaspberryPi up as an iBeacon, depending on your technical knowledge!