I dont know what to do with the little time I have to play Skyrim on weekdays, so I am usually playing MW3 on weekdays and Skyrim on weekends. What do you guys do when you have 15-30 minutes to play Skyrim?

If I have that little amount of time to play Skyrim, I don't play Skyrim. No way I could do anything of note in just 30 minutes. Game is way too deep for that.

I was about to write a serious answer, then I saw your avatar and lost all my respect for you.

I dont even bother playing any game until I have a solid hour or so free to put into the game.

Same here, i get in about 1 hour of skyrim per night...i play normally but usually never finish a quest in 1 sitting, i save and pickup where i left off
Quests involving dwemer ruins usually take me 3 nights to finish

If I bothered to log in, either do some selling/restock for the next adventure or just start hoofing it toward my next destination.

I've been trying to limit myself to an hour a night on weeknights. My thief character started sneaking from Riften to Markarth; the first night she got as far as someplace just east of Ivarstead. The second night she got to Whiterun, spent some time clearing out the exterior of Fort Greymoot, and is just west of that now.

In the process she's acquired ten wolf pelts, a couple sabre cat pelts, three mammoth tusks, a giant's toe, and countless flowers

Thirty minutes is enough time to clear out some dungeons...but not others. If you play fast you might be able to finish some short quests in a half hour - I can't say, I really don't pay attention to time when playing a game, unfortunately.

Oh that's easy do some misc quests! especially bounties. Most (not all) Misc quests take a relatively short time to do and give you a cool little reward. I usually have about 30-40 mins downtime in the morning before work and it's cool to knock out a couple of these before I leave. Get's me my little Skyrim fix till I get home

Yeah..I also have limited time with the game, as I have a two year old. But when get to play (about 30 mins per day if averaged out) I try to take it slow and enjoy every little thing about it. The scenery, the towns, small quests, etc... Start a quest maybe, buy or sell inventory, travel between towns, but never time to just blast out 2-3 hrs of endless play. Not sure if I want that to change. I don't get play enough to get bored or want to fast travel. Thinking this prolongs the enjoyment....