Can I send a telegram?
Or is that completely done away with?
Not candy grams or flower delivery tools.
Western Union no longer delivers telegrams, but yes you can do it.
I would be tempted to try itelegram:
https://itelegram.com/telegram/send/
I am still curious whether they have a fleet of motorcycle couriers as suggested by the picture, or if that is dramatic license.
So interesting.
I would love to do that.
And for $28.95 plus 75¢ per word, you can!
Seems like a lot of their current business is by people who need to send a legal notice or cancel a contract by telegram. Though surely there are still the traditional condolences, well wishes, etc. 30 bucks, though.
Does seem an outrageous amount.
Or, for the (relatively) lower price of $18.95, you can use them to send a “Mailgram,” which apparently amounts to, “give us your message, and we will print it out, put it in an envelope, and put it into the mail for you.” 
Find a local ham radio operator. They can do this- might even use Morse code. (Pretty likely need an older ham for that, though!) It’s free!
Turki Lurki
KO4HNB
It’s probably more the delivery to the addressee’s doorstep that you pay for rather than the electronic communication (which is, for practical purposes, free nowadays). So if your ham radio operator on the recipient’s side will give you the courtesy of transcribing the telegram on paper and then going out to physically deliver it to the addressee, then go for it.
More likely the ham operator on the recipient’s side will get the message, then reach for the phone, and call the recipient with the message.
A couple of family friends were ham operators back in the 1960s. They got messages from everywhere, bound for friends and family in their locale. They wrote them down, but then they’d make a local phone call, read the message to the recipient, and that would be that. If the recipient insisted on a transcribed message on paper, well, they might have to wait a week or two, until the ham operator had a reason to go to that part of town.
I recently sent my passport renewal application from western Pennsylvania to eastern Pennsylvania by priority express mail for $27.15. It arrived overnight, but perusing the tracking info it really should get there overnight by vanilla first class mail.