there are ac window units with the working parts hanging out and down
the window.

Are you referring to a mini-split-system? This will work for one room.
But I am thinking of cooling 3 rooms (two bed rooms and one basement).
I am under the impression that we need a HVAC professional to install a
mini-split-system. If we need to pay for a HVAC professional to install
three mini-split-system, we may as well ask him to install a ductless
split system that has three indoor air blowers that shares one air
compressor. I think this "may" be cheaper, and should be better in term
of cutting down noise the we will hear indoor, and we would not have
many ugly outdoor units hanging right outside the window.

how about an air handler put under your house and a duct
to each room, and the compressor outside a non bedroom area.. those are
pretty darn quiet. lucas

This works for the first floor. But we would have problem to run
ductwork to the second floor because we don't have an attic. All the
piping would have to go straight up through closets, kitchen, living
room...etc. We also need room for ductwork for return air from the
second floor. This would be an ugly work and would disrupt our lives
while the ductwork is being put in place. A couple years ago, I asked
HVAC guys to come over to see if they can install a central air
conditioning system in my house. But the proposed ways of running
ductwork were really not satisfactory to me and this has a lot to do
with the fact that my house doesn't have an attic...

Jay Chan