Using Find My iPhone from a computer when the phone is offline

call your carrier as well and get the SIM suspended, so nobody can run up calls or receive your login codes by text. while you're at it find the IMEI (on the box or the receipt), they and the police will both ask for it.

Yes, do it now. Sign in to the iCloud website on the computer, open Find Devices, pick the iPhone and turn on Mark As Lost. It queues even while the phone is offline and applies the moment it connects again, locks it with your passcode and puts your number on the lock screen. Don't erase it yet. Erasing removes it from Find My for good, so you lose any chance of seeing it pop up somewhere. Also turn on Notify When Found. Recent iPhones can still be picked up by the Find My network for a while after the battery dies, so the location may update even if the phone never comes back on properly. And ring the taxi company, honestly that's what gets most phones back.