My previous house had hammock hooks installed by a previous owner. I'm sure you've got somewhere that could work. Or enough floorspace somewhere for a metal hammock stand.

You should try the Hammock District, they may have some ideas.

I've seen standing desks that let you hang a hammock from the frame, but I have a feeling it makes for the worst hammock experience ever.

Not sure if it‘s meant to be, but your comment is a great joke.

Stud finder and some screw eyes

You can totally install a hammock on goalposts /s

Jokes apart there are free-standing hammocks. They take up slightly more space so that may not work.