I'm with the pack on this one. I confess I've never seen storage units as a permitted use (principal or special) within residential zones, they've always been in industrial or commercial zones in any community I've worked with. The two uses are inherently conflicting. While having self storage facilities nearby to one's dwelling would no doubt be convenient, the facilities would likely exert considerable negative impacts on their surrounding neighbors - namely traffic and more significantly with regards to security issues. The trouble is these facilities often resemble stalag 17, being surrounded by high fences (yes, sometimes complete with barbed wire!) and always with bright security lighting. The bright lights are understandibly necessary from a security standpoint - who would want to store their stuff in a facility easily accesable to crooks. On the other hand I wouldn't call anyone a NIMBY who didn't want to live next door to the Gestapo headquarters.
A community could create special/conditional use standards to accomodate such a use which would include lots of things like huge space buffers, light limits, screening, etc. but at this point I think one would be further ahead to say that if such conditions are possible to adequately protect residential areas, one should instead consider rezoning the property in question to industrial. However, the propriety of such a rezoning should always take into account the character of the area, existing infrastructure, future land use, etc....
I realize that communities often use multi-family zones as transitional buffers from more intense uses but I think it's another thing altogether to allow a use which is industrial in character within the multi-family zones themselves.
Lastly, and here I can only speak for Michigan only, I believe one of the standards for a use variance is that the land in question cannot reasonably be used in a manner consistent with the uses allowed in the zoning district (other planners may perhaps confirm or set me straight on this point). It is difficult to conceive of a scenario where one could have property suitable for accomodating a storage facility but not a multi-family use (which has been zoned presumably with that end in mind).