Where do you like to spend most of your time in the beginning(and possibly most of the time, regardless of being at the game's beginning or not) of various Elder Scrolls games?

Here's where I spend much of my time at lower levels and higher levels:

Arena - none, don't like any one city or area more than another
Daggerfall - Daggerfall(city as my base, the province as the only place I travel around at first)
Morrowind - Balmora and Vivec and the areas surrounding them
Oblivion - Imperial City and the area surrounding it

I like large cities.

I'm always a adventurer mostly in caves,dungeons,wilderness,ruins,etc. I cant stay in a city for too long.

I like small run-down villages.

Morrowind: Generally I tend to hang around the southeast of Vvardenfell (The Bitter Coast to Lake Amaya) doing odd jobs and guild quests.
Oblivion: The first thing I do is walk to the Market District, sell my starter loot, buy a weapon or piece of armor (spell if I play a magic-based character), and walk to Anvil. From Anvil, I take a stroll north and follow the border around to where the Black Road ends, staying the night in Chorrol. From Chorrol, I head north into this pass in the mountains that leads around Cyrodiil's northern boarder and comes out west of Bruma. From Bruma, I walk back to the Imperial City. So, I don't really have a base, but I do kind of "run the bases" in central/western Cyrodiil. I save the Valus and Nibenay for higher levels.

In Daggerfall I spend most of my time terrorizing those small kingdoms north of Daggerfall.

In Morrowind, I always seem to spend the most time wandering around the Ascadian Isles. No matter what type of character I make

When Iplayed Oblivion, I remember spending the most time in Anvil, actually.

Oh, and in Arena, I love to hang out around southern Hammerfell.

I went anywere and everywere in every game besides Daggerfall. Then I stuck to small cities in the Alik'

In Morrowind, Balmora was my base in almost every game. It's where the main quest hub is to start with, and later on Caius

In Oblivion, I tend to favor Chorrel as a base. There's an unusually rich supply of adventuring areas nearby. Lucrative ogre cave, lots of bandit caves, some ruins, a vampire coven, etc. Plus I tend to get in good with the general store merchant there, so I get good prices.

I've never been able to pick a favorite area in Arena.

In Morrowind the only places that I really stayed for any amount of time was Balmora, made my base that big house/shop that was across from Ra'Vir's shop and the guilds.

In Oblivion I probably stayed in the Imperial City the most when I first played, but Bruma and Cheydinhal were really close seconds.

Daggerfall... never manage to stick with it long enough to move beyond Daggerfall proper, actually.
Arena... never bothered to get it running. Should try it with my current DosBox tricks.

Morrowind, I never really move past Balmora for a base. It'd be nice to have one in a better location, but the map structure is terrible for the way I like to play. And it's so hard to retrace your way to a dungeon you skipped that I really don't need one elsewhere.

Oblivion: My early-game home base is the Imperial Market District. It's near the Arena (where I make my early gold), and there are caves and quests nearby. After I make some powerful friends, I migrate down to the Waterfront and then Bravil. Everywhere else is just a rest-stop I fill with sorted treasure. (Waterfront = books, Bravil = magic rocks).

In Morrowind I just tried to explore the world a lot more. So I didn't have any one place to hang out.

In Oblivion I tend to shop/sell in Chorrol (just a habit, haven't really bothered with finding the best shops as I mostly play as a thief anyhow) and I buy the shack on the Imperial City Waterfront as soon as possible, just to store any excess gear or ingredients and my alchemy equipment. The area south of Bravil tends to go under-explored in most of my playthroughs.

In Morrowind I usually have my base in Balmora as it is easiest to get a nice place there, but I love Sadrith Mora, it has everything you may need. As I mostly play Telvanni mages, the time always comes when I move to my own tower of Tel Uvirith, but I still love to visit Sadrith Mora at times. Other Telvanni settlements are nice too, but Sadrith Mora just gives me the best feel.

In Oblivion, I do not have a place I love, rally. I'm sort of fond of Skingrad due to its unique count and due to the fact that I like destruction which is the main interest of the residing Mages' guild. I also like Bravil, for it is a place none would expect to be a seat of a powerful wizard. But my base is usually in the Wizard's Tower near Bruma. That place looks quite nice with the view.

In Arena and Daggerfall, I don't usually take a base. I just go with the flow.

In Morrowind, I always take Foryn Gilnith's shack first, and then migrate to the *almost* empty manor in Balmora.

In Oblivion, I take the hollow tree stump in the IC Market District until I can afford either Skingrad or Battlehorn.

It's been a long time since I played "Morrowind", but I kept my loot in the orc mansion that has the merchant, Creeper. I enjoyed exploring tombs and ruins for much of the time, and I liked the Ascadian Isles region.

The first time I played "Oblivion" a few years ago, I used the Knights of the White Stallion hunting shack as my base and bought/earned the Anvil mansion. This time around, I'm using the hunting shack and bought the Leyawiin house out of curiousity, but regret spending the money now. I'm not going to bother to get the Anvil mansion this time around, as it's beautiful but too large for one person. I don't like the IC enough to make it my base.

In Arena I was a Nord, so I stuck around Snowhawk the most.

In Daggerfall, I usually either had a house in Daggerfall city near the fighter's guild, or a house in Gothgate (Daggerfall province) near the market, or a house in the city of Anticlere close to the mage's guild.

In Morrowind I would use one of the huts in Ald Rhun because I could get there quickly from Solstheim.

In Oblivion I had the house in Bruma.

Never played Arena
In DF Dwynnen since I liked the Order of the Raven most of all the knightly orders (purely on the basis of it's name)
In MW depended on the character. Probably Ald'ruhn most often
In Oblivion the IC