I'm a little unclear on what you mean. Actually, scratch that, I know exactly what you mean (and it's a damn good question), but I'm a little unclear on what direction and how far you're asking about. See, the senate was not really a governing body, it was an advisory body that issued councils (consilia) to sitting magistrates. It had few official powers, although the influence of the senate (which was made up basically of ex-magistrates and former magistrates awaiting candidacy for further magistracies) was quite large, as typified by senatus consulta, which often had the virtual force of law, though it was not actually law. Laws were passed by the citizen assemblies and were written up and proposed by magistrates. The real governing of the city was done by the magistrates, who all had their own particular functions--the aediles maintained markets and some facets of infrastructure with their staff, the praetors presided over law courts, etc.

However, I suspect you're asking about forms of local government within the city. Which is to say how neighborhoods and so forth were organized and all that. If that's what you're asking about I can still help you out, but levels of organization, official or not, pervaded all levels of Roman society, and I'd like to make sure I'm understanding you right