The unicorns are found in one of these following locations;
1. Large Parks
2. Small Parks
They are more likely to appear at large parks then small ones. They appear at 8 pm and disappear at 4 am. There is a %40 chance for a unicorn to appear in one of these locations every night. Having a Sim with the "Animal Lover" trait helps a lot. If there is a Sim with the "Animal Lover" trait, a green light appears above the location with the unicorn (in Map view). It is so obvious that you can't miss it. In Appaloosa Plains, the unicorns are most likely to appear near the waterfall.
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Unicorns can appear at any time any day, they're not around everyday. Usually when they appear, it's a lot later, midnight to the early hours of the morning. To find them, check your map around that time often, and if a unicorn is out, you will see a glittery cloud hovering above an area. Wherever that cloud is, it means a unicorn is there. They don't appear every night, so don't count on one to appear all the time! The clouds are found a lot in fishing areas, but they are big and quite apparent to see on your map, so you really can't miss it.