So, just started Morrowind, and I've yet to see a nice house that isn't locked or belonging to someone already.
I wanted to have a house in the city of Balmora as it's close to traders and Silt Striders.
Is there any abandoned house I can claim as mine or is there any house where I can easily kill an NPC and take it over?
I'd rather not follow some huge quest line to get a house.
Just need a place to store some stuff I found and a real house would be preferable.

Well, it all depends on whether or not you want to be a murderer. Just make sure that you taunt them in to attacking you first so you aren't a murderer (technically).

If you see a house that is owned and the owner is not present, just move in. I've lived in a house where the "owner" continued to walk around right outside with no problems whatsoever. There's also a house in Balmora where the owner is already dead.

More than that would be spoilers.