I like having my town in real-time because it feels like the town is living along with me. I like turning the game on in say, winter and having snow on the ground, or on Thanksgiving and having a cooking turkey in my town!
I like to stay on the current day or a day close to it, but I keep my time kind of random. Usually early in the day so I can order stuff then TT to get it all delivered in the same day for trades.
mine should be set with real life day/time but I wasn't able to play for a while so it's like 3-4 days off from the current date. and I'm too lazy to TT and keep up with villagers if they want to move out and such.
My main town is one day ahead and 3 hours behind. This way I can play the holidays with my villagers and than enjoy it with my family. It's set 3 hours behind so I can play bug/fish off and other evening events. I play at 8pm and would miss a lot of events.
My other town is set 3 months ahead and the clock is set for the morning turnip prices. It's nice to escape from the snow.
I don't really TT; sometimes I do in order to get a villager who's moving out to move out quicker, but that's it. I set my time to my current time, though I'm thinking of setting it a few hours behind so I can play later in the day.
I usually have mine set to the actual date and time but I know I'll be way too busy during Christmas to play on Toy Day so I'm gradually playing a day, then fast forwarding one day per day so I can play on Toy Day. The time is always set to normal time unless I need to move the time back some to open shops.
Then I just move time back to normal, and after Toy Day I'll end up moving the day back to normal.