Yes, students commonly take the SAT or ACT at high schools other than their own and for many reasons. For instance, a high school may serve as a test center on some test dates but not others, or a test center may be full when students don’t register promptly. Geography can be a factor, too. If you don’t live close to the school you attend, you don’t necessarily want to get up before dawn on a Saturday to get to the test on time. (Of course, what teenager wants to go to ANY test ANYwhere on a Saturday?) 😉
The big advantage of taking a test at your own school is familiarity. You won’t worry about getting lost on your way there, and you’ll certainly be able to find the cafeteria or library or wherever the test is being administered. You’ll also see friends and teachers you know. For most students, this is reassuring … but it can also be distracting. (I’ve even had students tell me that they intentionally avoided their own high school because they didn’t trust the level of supervision and predicted that there would be erasers soaring through the air and test answers exchanged in the bathrooms, so they opted for a more “sedate” school in another district.)
Regardless of where you take the SAT, you will have to meet the College Board’s identification requirements. But at a high school where no one knows you, it’s possible that your identification may be scrutinized more closely than it might be at your own school. So just make sure to read instructions carefully and show up at the test center with a clear I.D. that leaves no doubt that you are the student you claim to be.