I think everyone already knows that you can check the date and time when you go to the menu screen. Well, when you start a New Game from the main menu, (and after you play through the beginning on the cart to your execution) when you pull up your menu I'm 99% positive the game starts you off in the middle of the month of Last Seed.
Well, for those of you well versed in the lore of Elder Scrolls, you might remember that "Last Seed" is the equivalent month of August for us (you can see all this kind of stuff at The Imperial Library). I'm going to have to check on what specific day of the month it is, I'm pretty sure it's around the 15th or so, but here's my thought for you all who want to do something unique and, in my opinion, awesome:
Start a new character on that date, and play only one day at a time in the game each day to keep your character at the same pace as in real life. I would suggest not fast traveling (as that skips time ahead), and trying to do things that you normally would such as walking through towns, sleeping every night that you can, and so forth.
I did this exact thing in Oblivion 5 or 6 years ago and it was an incredible experience for me. I literally took one character on an adventure for around 3 or 4 months and completed the main story. I took it very serious in the fact that I tried to things that would seem to make sense to an adventurer. Like sleep every night in an inn if I didn't own a house at that town, try to sleep at a campsite if it was getting close to midnight and I was still on the road, I would eat and drink something most nights, not leave towns for the next one until the morning and travel by day, etc.
This has been too long already but I'm interested in hearing your ideas on how else you could make this realistic and if you like the idea. One last thing I'll include is this: you might be thinking there will be days when you can't play. That's not a problem either. What I did on those days was just assume my character was staying in that given city for a whole day not doing much of anything except maybe people-watching, and then the next time I would play, I would just sleep or wait for 24 hours or however long it took to catch up with the current date.
Let me know what you think if you're interested. I'm going to find out what exact date the game starts on.