although there are references to shinar as the dwelling place for a physical tower, i do not beleive there is a physical tower to be found.
when going back to the hebrew translations we see differences in the english translation.
when we insert the hebrew we find many metaphorical values.
IMO the language spoken of is that of the science and magic of kabbalah, the tower being built was an attempt of the sharing of this divine language(kabbalah) to build a formation to reach the upper worlds or heavens as described in abrahams sefer yetzirah- book of formation, through the ten sefirot were emanation down to the physical plain (earth)that defined the pathway from GOd to man, if men during the time of the story of the tower of babel were sharing the language and science/ and or magic of kabbalah, they were trying to build a tower in reverse through this language to reach back up to the upper worlds or heavens where they believed God to reside as to make a name for themselves in the signature of creation.
so metaphorically speaking the tower was a series of incantation using the diagram of the hebrew alef bet and the principles of either kabbalah or sefer yetzirah to make a signature in the code of creation to extend back to His throne so as to make a name for themselves in the heavens.