Where are the best house locations in Skyrim?
Windhelm probably offers the highest convenience factor. The market neighborhood, directly to the South, offers access to a full set of outdoor smithing equipment, as well as an Arcane Enchanter, at least three 'high-value' merchants (two general goods, including Niranye who is a Fence, and a Blacksmith), all without a loading screen. The house itself offers both Alchemy and Enchanting facilities, as well as the highest number of display racks for equipment of any home, and Windhelm offers an additional battery of merchants over in the Grey Quarter on the eastern edge of town.
Downsides include the somewhat high price, long distance from Windhelms fast-travel point, the prolonged string of quests required to buy the house (you basically must resolve the civil war), and the potential for significant bugs related to the Blood on the Ice quest, in which the house is involved.
Riften deserves an honorable mention for Thieves Guild members. While it lacks smelting services, the upgraded Ratway, with it's 4 additional merchants, puts somewhere in the neighborhood of 12,000 Merchant Gold in close proximity - easily the most of any city. Those who choose to take the moral high-ground may find the mercantile climate of Whiterun to be more hospitable however.
I would say Whiterun, as it is the first house availble, and has almost everything close-by.
The only vendor not availble inside Whiterun is the fence, which is located in the Honningbrew Meadery.
The Arcane Enchanter and Spells Shop are located slightly away from your house inside Dragonsreach, but there's also an alchemy station located in that place.
I've found the house in Markarth is really good. It has an enchanting table. It has a satchel on the stool near the alchemy table. It has a really close general store and a somewhat close blacksmithy. The smelter is between the smith and a nearby mine.
The downsides are the political unrest in the city (situation is usually sorted out by the time you get the house) and a lot of vertical navigation (dwemer love their stairs).
Here's how I navigate those locations in Markarth.
Enter main gate: Here's the general store on the right and Inn across the bridge.
Go to the right of the general store and up the stairs. Go up and up and up to get to your house. If you didn't get to your house, you didn't go up enough.
Go back to the main gate, cross the bridge and go to the left of the Inn. Follow that and you end up at the blacksmith with the smelter below outside the mine.
Places to cure disease: The temple of Dibella and shrine of Talos are in the middle pillar of the city.
My normal loot sell-off/drop-off route is: Fast Travel to the keep. Walk to the smith, then the general store, then my house.
By comparison, WhiteRun is Fast Travel to the gate. Walk to the smith, then the general store, then the enchanting table in the keep (yuck), then my house (far away).