My first few days in Morrowind always look pretty much the same: Explore surroundings of Seyda Neen, claim tax collector bounty, hop over to Balmora, grab a few spells, might do some faction quests or find the puzzle box if I'm sticking to the main quest.

But I want to do something else entirely this time, but I'm not sure what I'd like to do.

What do you do when you start a new character to make it a little more interesting? I can imagine using an old Velothi tower as a base of operations while being a Telvanni member, but I'm not interested in another mage playthrough at the moment.

I'd suggest an alternate start mod. Too bad Arthmoor didn't make one for Morrowind though. If you're on PC, though.

I made an Argonian diver a while back and I immediately hopped in the water with him and rarely came back to land. That was different.

If you'd rather have something other than Seyda Neen though, I also suggest an alternate start mod; like http://mw.modhistory.com/download-37-6583.

I've mentioned this before, but my favorite thing to do at the start of a game is to take my characters on a tour around the coastline of Vvardenfell. It's a kind of rite-of-passage. Starting in Seyda Neen, we run and swim east through the Ascadian Isles, north through Azura'a Coast, west through the Sheogorad region, across to Solstheim, around Solstheim, back across to the Bitter Coast and, finally, down to Seyda Neen. By the time they get back to Seyda Neen my characters have gone from level 1 to level 6+. I think it's great fun. I wish I could do the same thing in Oblivion and Skyrim.

RP'ing it, one character got a hazy glimpse of the Vivec Foreign Quarter from the Seyda Neen silt strider platform (I use MGE with fog distance set to 5), and went to check it out. Another wanted to get as far from the clutches of the Empire as quickly as possible, and managed to make his way North along the coast to Hla Oad before turning inland along the river; to his surprise, he found himself in Balmora anyway. One found a soulgem and wanted to find out more in Balmora, but one local merchant mentioned that the Telvanni seemed to know more about them, so you can guess where he ended up heading. Yet another took the silt strider to a random destination. What happened from there was totally dependent upon what they found and heard. On the other hand, half my characters do the "usual routine". Pick out something in a conversation or that they see and follow a train of thought about it, wherever it leads.