For some reason, before I enter a town/city I always unequip my helmet and weapons.
I don't know why I do this but I always have.

As I enter my houses I always change into my robes and shoes aswell.

Same here. I take off the helmet and weapons, usually find a room somewhere and change into clothes and equipping nothing but a dagger. I also have a better time immersing myself if I go into 3rd person. I go back into 1st person when I go inside buildings.

When I get into a town, I symbolically call that town my "base" until I've done every quest I can there. One day I take a bounty and go out adventuring, the next I'll remain in town and talk to everybody I walk by and/or chop wood.

It's actually a really good balance. You don't get overwhelmed by a truck-full of tedious fights, and you don't get bored talking to NPCs.

I'll normally take off my helmet, shield( I imagine that I place on my back) and put my arrows away unless the character is mainly an archer. If its the town that I life in then I'll head home grab my street outfit and put my armor away. At my home town I'll do some crafting and shopping and just live there for a day. Any other town if I'm not looking for work I'm just stopping there long enough to resupply.

I roleplay so it depends on my character, not me.

Some characters change into "street clothes" before entering a town, some leave their armor or robes on. Some walk everywhere inside a city, some walk only inside of buildings or inside of certain buildings, some run everywhere. Some sleep in Inns as soon as they get into town, some never sleep in inns. Some talk to everybody they meet, some talk to a select few, some talk to nobody. It depends on the character.

My current character doesn't really do anything differently - as a mage, she doesn't have armor to remove of weapons to put away. If she's entering Whiterun, however, she'll head to her home and change into some different clothing.

Wipe all of the blood off of my armor. The townsfolk tend to frown on that sort of thing.

They never like my dead thralls either....so judgmental. Like they've never experimented with killing someone and possessing them....

That's actually not a bad thought, long as you remember to re-equip the armor and stuff when you depart.

I very rarely fast travel, so it's kind of a habit to re equip everything as I leave now lol

This for me. It also depends on the situation. Is the character just passing through, or will he/she stay for a while, did they come to shop, visit the inn, the temple, the Jarl?

Hit the tavern for rumors and mead