If you have a good relationship with your landlord (and intend of staying some time), might be worth discussing collaboration and leaving the AC when you move? A unit with AC would command a higher rent for the next tentant.

Through wall designs, like you see in cheap motels, require an opening in the wall.

Mini-spits have an outdoor unit and an indoor unit connected by two hoses. The indoor unit basically screws to the wall. You do need a hole through the wall for the hoses but that's it. As a result they are cheap to and quick to install. They are also very efficient.

> You do need a hole through the wall for the hoses but that's it.

That's what they're pointing out. It's not a huge hole but it's still a hole going through the wall, and if they rent and buy the unit with their own money they'd be leaving with it, leaving that hole in the exterior wall. 3" is probably on the upper bound of what you need but it's not wrong. And it's not like the landlord would be much happier with a 2" hole.