I know that race doesn't greatly affect gameplay except some powers and resistances, but I was wondering about little ways how it affects interactions with NPCs and quests in the game.
I know if you play an Altmer and kill Ondolemar, the Thalmor Justiciar in Understone Keep, then a courier will deliver a small inheritance to you. On the other hand, 3 Thalmor brutes callously attacked me for standing close to them on a road -not very nice at level 4 but you'd think they'd be less likely to smack another elf around.
You get an inheritance if you befriended a particular character who has died, regardless of your race.
I also noticed the barkeep in Riverwood would not trade with me at first but I'm not sure if that had to do with a factor other than my race -like the time of night or if he had to sneak off to the outhouse once I left the inn.
I love subtle touches and atmosphere like this.
I agree, I think the subtle touches were done very well. Playing as a Dunmer protagonist, some of the guards ask "what is it, elf?" when my character crosses their path. The elves in the Gray Quarter didn't have a problem with my protagonist, and one of them warned me that it was difficult for "those such as us." The Thalmor still view themselves as high and mighty over everyone else, and seem to have no problem trying to kill another elf.
While not directly related to the protagonist, the history of the Harbingers mentions men and women of different races becoming Harbinger as well, and the reaction some people had about that, possibly as an explanation for setting a precedent for non-Nords becoming members and Harbingers of the Companions.