This past winter, during a kitchen renovation, I had a Mitsubishi mini-split installed on my first floor. There is one unit outside the house, and a wall unit in the kitchen (the back of the house) and another one in the living room (front of the house.) It was kind of pricey, but I'm so glad I did it. It cools the entire first floor and is absolutely silent. In the kitchen the wall unit is centered above the back door, and in the living room it's high on the wall to one side near the entry from the foyer. People don't even notice it. On the second floor the bedrooms are cooled by window airconditioners. You should look into a mini-split. I love mine, and as a bonus I can use them as additional heating units (you just adjust the thermostat to a higher temp.) I probably would never need to do that, but you never know.

Look into it, it's a great alternative to central air and all the ductwork.

Mimi, thanks for your response. Can you tell me how many square feet the two wall units are cooling? Also, I'm curious why you didn't intstall them upstairs as well. And it sounds like yours are quiet. I've heard differing things about the sound, but I'm hoping for something quieter than window air conditioners!

Be sure to look and listen to a mini split before installing one.
If you have attic space you can run conventional ducts there for AC.
This is a location that duct board is better than sheet metal (the lower mass reduces the amount of heat the ducts can hold).
The high velocity systems (Unico and Spacepak) can work well if you need to run lines from an attic past a second floor to the first floor.
The equipment is more expensive, but the installation is far less damaging to an older house with plaster walls.

The two wall units cool the entire first floor, about 800 to 850 sq. ft., very efficiently. I can feel the difference within a few minutes of turning the a/c on when I get home from work and it's 90 outside. I find setting the thermostat at 70 deg. is usually fine. I don't leave the a/c on when I'm not at home. The window a/c in the upstairs bedrooms are fine. Installing a mini-split to cool them would have meant putting another unit on the other side of the house. The ductwork would have been on the outside of the house to each bedwoom. Additional expense ($$$) and the window a/c's work just fine.

On the first floor, the ductwork in the kitchen is inside the wall, since it was demo'd down the the studs. However, the ductwork leading to the living room wall unit is on the outside side wall of the house: runs along the ground from the outside unit to where the living room is, and then straight up to where it connects to the wall unit. It's on the side of the house and not very obtrusive. I can't tell you what a difference it has made.
Prior to getting this I had a big window unit in the LR that actually did a good job of cooling, but was so noisy that it drowned out the TV sound. Now, all is cool and quiet.

As part of a kitchen /bath addition I did on a home we installed a two zone Unico high velocity system. The HVAC guy ran 8" main trunk line around the basement and attic and cut in outlets that went to each roon. There were 1 to 4 outlets per room, based on room size. One outlet per bath. The system has been in for about 5 years and works well. How smooth the install goes depends on the company doing it or the guidance and direction you give them. As the GC I wasn't too impressed by this company. I had to "suggest" main duct runs, help with return placement and overall supervise the workers. You want a supervisor on site, not just some workers who don't understand the big picture.
The system ran about $12,000. with a 2 1/2 ton unit on the first floor and a 1 1/2 ton for the second floor.
Ron