How can I have an object that just moves randomly around within a set radius?
Like a monster patrolling an area? Well, I'm assuming you know how to move your monster etc, so lets talk about limiting its movement radius.
You could make a new GameObject and call it "AreaCenter". It will have a script containing a variable called "Radius", a variable you may edit and will represent the area radius, of course.
So, put the AreaCenter object in the scene, and then put the monster close to it. The monster should have a script with a variable looking for a Transform object. Link the AreaCenter object to such variable.
Now I guess you will make the "moving route" part of the monster. Just remember to use Vector3.Distance (see docs) to check the distance between this monster transform and the AreaCenter transform, if the distance is greater than the one you set, try to change the monster's route again.
Technically, the monster will never leave the radius.