As the thread states, what is that you do? Do you get a feel for the city? Enter every buidling to see what inside? For roleplayers, do you head for the inn?

Try to find the blacksmith and general store.

Watch the scripted atmosphere events designed to define the town for you. Beheading in solitude, mob in Morthal, save the girl in Markarth, the nords hassling the dunmer woman in Windhelm ... with the exception of Winterhold and Falkreath, every town of note has something like that.

Then I tend to look for whatever brings me to town unless it's evening in which case I go to the inn and rent a room.

Inn, yeah.

Try to find shops and get a feel for the city.

Look on UESP or the Wiki to see which characters are/are not essential, and I kill all of the nonessential ones. Then I reload a previous save, and head for the inn.

I head to the Inn, rest for a day, and help out the city/town. I stay there for a few days then head off.

Depends. If the town isn't my intended destination (I could be walking from Whiterun to Soltitude, passing through Rorikstead) I might just keep on walking. Unless the sun's starting to go down, then I'll rent a room for the night before moving on.

If it's my intended destination, then the town's inn is still my preferred choice. Once you get a (temporary) roof over your head, you can get yourself situated and explore/meet people.

Just got there from travelling, so I head to the local Inn or Tavern and get some food and rest. Then I wait for shops to open if they are not already and start selling my wares to the local shopkeeps.

Why would you kill the non essential NPC's?

Usually, I'll explore a bit, then proceed to the local Jarl, do some quests, purchase a house and so on...

I find the nearest vendor.