When I first played Morrowind, I had the brightness set up high. As a result, I never had to use a torch when exploring dungeons or caves. Now I'm trying to make it more realistic by turning down the brightness, and now it seems like twilight outside when it's high noon and cloudless. Isn't there some middle ground without having to change the brightness all the time?

You could try using some shaders with MGE, I haven't done this myself though, I tried and gave up because I was impatient :confused:

Wierd, I never had this problem. Try adjusting your screen perhaps?

It is going to be different for each computer, but suggest setting your monitor Brightness to an average setting (probably default) and then lowering Morrowind's Gamma Setting by just a little bit.
That usually gives interiors a nice gloomy feel, and keep outdoors bright enough.

But, you do realize that is only the tip of the iceberg.
There are many, many ini tweaks you can do to make the game darker/brighter in certain areas, and at certain times.
There are also a few mods that completely overhaul the lighting of the game, making it more realistic and dramatic. (Not to mention shaders with MGE)