I'm not sure if this is what you're looking for, but you may be interested in the graffiti from Pompeii. Because the whole city was wiped out at once in a volcanic event, the ash did a pretty good job preserving things that would have otherwise probably not been preserved.

From a cursory search, this seems like a good repository of what they found when excavating it:

http://www.pompeiana.org/resources/ancient/graffiti%20from%20pompeii.htm

What makes this interesting to me at least is that this is the type of language that the common, 'vulgar' folks would have been comfortable with, instead of the writing of some educated official that tends to be the bulk of the historical record.

I have no insight into linguistics to offer, but reading through the subject matter linked above is at least entertaining.

What you are referring to is called "Vulgar Latin", where vulgar means vernacular in it's original sense and not rude as in the modern context. Vulgar Latin is a broad term for the many localized dialects of Latin around the empire. I have not done extensive research on this so I can't point you to any exact sources on this, but this is a pretty widely accepted definition and I'm sure you won't have trouble finding additional information on Vulgar Latin.

Also of note, Vulgar Latin does not refer exclusively to dialects which evolved into modern Romance languages, however towards the end of the empire, some of these dialects do become the basis for many modern day Romance languages.

Classical Latin had pressure to conform to the standard, and so stayed pretty static. Vulgar Latin was more organic, and IMO there certainly developed regional variations between cities. The problem is that very few things were written down in Vulgar Latin, so there might not be enough data to say for sure what the differences were.