So I just got myself a new iPhone 7 Plus and I am having some issues with Airdrop. While I can send files to other devices just fine, the other devices cannot see my iPhone. Airdrop is turned on for Everyone and I already tried rebooting the device. Maybe there's some other setting that I am missing?
Try going into Settings > General > Reset > Reset network settings.
That will also clear out any remembered WiFi networks so you will have to re-authenticate. But I have found that doing this often fixes a variety of network-bound problems.
Erasing all contents and settings and setting up the device as a new iPhone did the trick. (It had been previously restored from a 6S backup).