We bought one for an addition that is essentially a great room with a cathedral roof and it works great. It's one of the Mitsubishi ones.
We have central air upstairs only, and that was generally good enough to cool the downstairs as well. But the air wasn't getting into the addition because it is further away and only has a regular-sized doorway, which is often closed.
When a friend who has an antique house with no A/C saw how well it worked she had a few installed in her house and loves them. IIRC she has one for the entire downstairs and got two for the upstairs based on their recommendations, because the bedrooms are more closed off than the downstairs. In retrospect she said she probably only needed one upstairs, but she lives alone, so YMMV.
Go to the Mitsubishi website and they will tell you the dealers/contractors in your area. Our heating oil and A/C people were one of the dealers in our area so we used them. Tell them your square footage and needs and they will give you recommendations. Make sure you specify that you only want air and not heat, because the units without heat are less expensive. You will also need an electrician. The company selling the units will have a list of them of whom they approve for these installations. Make sure you get a good quote directly from the electrcian. Our electrician charged more than the A/C people estimated he would, which of course made the whole project more expensive than I expected. But worth every penny nonetheless. Quiet, effective and blends into the wall for most people.