There are some websites that have free APIs. One is JSONPlaceholder, but you can easily request access to some others. For instance, Strava offers some for those interested in developing applications from running / swimming / biking data; all you need is an account, which can be made at no cost!
Now, depending on your knowledge, if you have some web development experience or are willing to learn about it, I recommend using Node.js and setting up a localserver on your network, or perhaps on a hosting platform (e.g. Firebase, which I believe is free). From here, you can set up routes which handle HTTP requests, or the like, from which your students can send GET requests to. And since you would set up the routes and the data to be returned, you could tailor and personalize the data and the routes to the students (e.g. have a hypothetical endpoint
<YOUR-FIREBASE-APP>.firebaseapp.com/Jeremy which would return info about your student Jeremy).
My opinion? As a student, I would not only be impressed by a teacher who could do something like this, but also personally intrigued as to how routing and servers work. But, hey, maybe that's just me :)