Window bars can make window a/c installation tricky, but not necessarily impossible. A recent thread on Brownstoner.combreezes through some workarounds:
Modify the bars in at least one window. You're going for a potbellied or boxed out look. The cost could be as high as $700 to $800 per window. Then you have the cost of the air conditioner and the window installation.
Cut a hole in the wall (if you can get permission, that is). It isn't cheap, since you need a sleeve, probably a new socket and the more-expensive, less-efficient thru-wall a/c. But, it does seem more "finished."
Buy a portable a/c. It sits in the room and takes up floor space, which isn't great, but at least one renter (with window bars flush against the building) said it worked well. Added advantage -- you can store it in the off season.
Window bars are mainly found in street-level apartments, where installing an a/c means literally opening a window on street noise. One commenter advises buying a high-quality a/c like Friedrich Kuhl, "which not only runs quieter but dramatically reduces the amount of noise that comes in through the unit."
And you might want to find an alternative to those plastic accordion-style wings on either side of your a/c: "I never use the plastic wings that come with the unit. I cut 3/4 plywood to size, paint and use mortite everywhere. Like keeping out the cold in the winter, you need to keep out the heat in the summer. This will also cut down the noise a bit."
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