There is no Mesopotamian length unit which approximates a mile. In the standard system introduced by Sargon of Akkad (c. 2350 BC) and in use to the end of the Old Babylonian period (when the vast majority of 'Babylonian' maths comes from), the length units are (in Sumerian, Akkadian and English):
Sumerian Akkadian English 1 she 1 uttetum 1 barleycorn c. 3 mm 1 shu-si 1 ubanum 1 finger = 6 barleycorns c. 17 mm 1 kush 1 ammatum 1 cubit = 30 fingers c. 0.5 m 1 gi 1 qanum 1 reed = 6 cubits c. 3 m 1 nindan 1 nindanum 1 rod = 12 cubits c. 6 m 1 USH 1 ... 1 ?? = 60 rods c. 360 m 1 danna 1 beru 1 stage = 30 ??s c. 10.8 km
There are other units too, but these are the main ones. Even in Akkadian texts (such as OB maths) metrological units are usually written in Sumerian because it is quicker. In general you need just one cuneiform sign to write a Sumerian word with no grammatical indicators, but several to write its Akkadian equivalent, because it has to be split into syllables. So the length '60 rods' is always written with the sign USH (which might be read in several different ways, as most cuneiform signs are polyvalent), so that we've no idea what its Akkadian equivalent is, and therefore how to translate it.
After c. 1600 BC there are several different competing systems, some having impractical divisions such as 14 cubits to a rod. (Because 14 irregular, one can't divide nicely with it in sexagesimal.) For more details, the definitive survey on all Mesopotamian metrology is:
M A Powell, "Masse und Gewichte" in _Reallexikon der Assyriologie_ 7 (1987-1990), 457-517.
Don't be fooled by the title - it's in English.
I'm not quite sure what you mean by the question "how is it tied to OB geometry?". The basic unit of measurement in OB maths is the rod (just as we use the metre) and although lengths are usually given in the mixture of units I listed above, for calculation purposes they are converted into nindan. For instance, a student's exercise on finding the area of a square:
The length of a square is 1 rod, 4 cubits. What is its area?
The student writes this as 1;20 rods (perhaps using a metrological conversion table to help), and calculates the square of 1;20 = 1;46 40. This is converted back to area units: 1 2/3 plots, 6 2/3 shekels.
(NBC 8082, from Neugebauer and Sachs, _Mathematical Cuneiform Texts_ (New Haven 1945), p 10. For more examples, see Neugebauer and Sachs, "mathematical and metrological texts", _Journal of Cuneiform Studies_ 36 (1984), 243-251.
I hope this answers your question, at least in part.
With best wishes,
Dr. E. Robson Junior Lecturer in Akkadian The Oriental Institute University of Oxford firstname.lastname@example.org