I don't quite understand your question. Good synonyms for distinguish here would be ascertain, discern, identify, figure out, determine.
Your original sentences:
Once I got to that town I could distinguish the cultural differences between the neighbourhoods. - good but I took out different
Once I got to that town I could clearly tell the cultural differences between the neighbourhoods. - good but I took out different
Once I got to that town it was easy to tell apart the cultural differences between the different neighbourhoods. - Once I got to that town, it was easy to tell the cultural differences between neighbourhoods apart.
Having 'differences' and 'different' in the sentences was redundant to me.
Does this help?