I haven't tinkered with electronics since I was about 15, so I'm quite new to Arduino and would certainly consider myself a n00b. I want to build a device(s) that tracks when another device (identical to the first, but has been paired) is a certain distance away (example 10 meters). Once they are more than X meters away, I would like an alert (LED indicator and vibrator) to go off.
I would love some guidance on whether this would be feasible with Arduino, and what kind of sensors you would recommend?
Your specifications are quite vague, but it seems that in general, what you want to do is not feasible on a hobby budget. Object localization is of intense interest but the best we can do out-of-doors is still GPS, which at best has about 3 m accuracy, but often shows very large errors and may not work at all. Accurate indoor localization is very difficult. There are no sensors or radio modules that can be used to accurately measure distances of several meters between self contained movable objects or robots (except perhaps laser range finders, and those have to be accurately aimed).