There was a representative, a leader, from each tribe. Why wasn't there a Levite presence among the 12 meraglim? Does it have something to do with the fact that the Levites have no dedicated territories?
I heard a position before that since the people wanted the land to be explored, and Levites had no inheritance in the land, the representatives from Menashe and Efraim were chosen separately, without the representative from Levi, as is commonly done when dealing with questions involving land. For example, when the land was divided by Yehoshua, this was the representation of the tribes as well, and so too in the census in Bamidbar - since it counted people participating in the army to conquer the land.
This position fits well for the opinions that hold that parsha of Korach came before the spies (Ibn Ezra I think), since the explicit wording that kohanim have no share in the land is mentioned there (perhaps there is an earlier mention somewhere in Vayikra, but I don't recall it). For others, one would have to assume that it was known that Levi would not get the land for this answer to work.
Mystically, the Alshich alludes to (and the Arizal writes it more openly) that the 12 spies were incarnations of the 12 brothers. Rav Moshe Wolfson writes in his talks (see the English one on seudah shlishis for parshas Shlach) that since Moshe prayed for Yehoshua and changed his name, he made Yehoshua his personal representative, and the soul of Levi was connected to Yehoshua (who was originally from Efraim). On the other hand, when listing the spies, the prefix "for tribe of Yosef, for tribe of Menashe" is used for Menashe, but "for tribe of Efraim" only is used for Efraim (no mention of Yosef), to hint that Yosef's representative was from Menashe, not from Efraim. So in a mystical sense, there was a representative from Levi, - Yehoshua.