I am non-tenured and have been offered a tenure-track position at my current university, but I don't want to stay here long term. What should I do?
There's nothing to prevent you from accepting the TT position (which presumably carries better pay and more prestige) while still pursuing positions elsewhere.  Indeed, having a tenure-track position may improve your chances of getting an offer outside, or may increase the leverage you have to bargain with if offered something elsewhere.  And there is absolutely nothing wrong with accepting the TT job and then leaving (after a year) for another position.  Your department head might not be happy, but this kind of thing is not viewed negatively by the academic culture at large.

In short, I see no downside for you to accept the tenure-track offer.