This is my 2nd time this year with Jan and family, and again my trip was even more fun now that I had a better understanding of the neighborhood as well as venturing outside of the Da'an/Yongkang Street area. You can't beat Jan's location because it's minutes away from the Dongmen metro station and of course, the fun places to eat off of Yongkang Street.
I highly recommend checking out the morning market of Dongmen (just 1 block north of the original Din Tai Fung) which runs from 7 am – 1 pm daily I believe. There's also an even better morning market outside of the Shuanglian metro station (about 5 quick stops from Dongmen station and only 20NT/$0.63 usd. In the evening, there's a nearby night market that's more for the locals called Shida Night Market.
The beauty of Yongkang Street is actually walking through all the little alleyways and finding a cafe or nice eatery. Check out "Who's Cafe" – great spot to relax, drink oolong tea in a nice cafe.
Enjoy.