Check your city’s website. Most cities devote at least a portion to their website to listing what adult education classes they offer. Often those classes include fitness classes, and sometimes they include Pilates. Go to your city’s official website (the web address should end in .gov) and enter “Pilates classes” in the search bar.
Once the results page comes up, you should be able to sort the available classes by the time they're offered, where they're offered, and the cost of the classes. Even if you can't sort the results, that type of information should be available for each class - it might help to write them down on a piece of paper so you can see all of the relevant information all at once.