JJ Bakery. (Chain--tried the Arcadia location) This is a California chain that makes Taiwanese-style breads and cakes, much like Bread Corner here, but done much better. This is a good place to hangout while you wait for your text from DTF. You can also buy some breads and cakes to go. I rather enjoyed their egg tart, as the crust was a just-right flakeyness to it for me. I also enjoyed their wife cake and their taro custard bread (much later on of course) .
I've heard about the epic waits at DTF but had always been lucky with the wait (Arcadia Baldwin location) by going at slightly off times, never having to wait more than a few minutes...I guess it was a "weekend" day for most people, because the wait was already partway down the plaza. We didn't even bother to find out about the length of the wait and instead grabbed some items from JJ Bakery (it's in the same plaza).
I love DTF, and I agree with you- the XLB are the reason to go. My sister is in LA and it is a regular stop for us. We waited a long time last winter break- but we went to JJ Bakery (delicious and cheap) and then walked around the neighborhood for a bit.
In addition a full suite of typical Taiwanese bakery items, J.J. Bakery in Arcadia (I've only been to that location) also has a limited selection of cooked/hot breakfast/dim sum foods (at least in the morning), making it an even more attractive alternative to Din Tai Fung when the lines are too long. We've had the turnip cakes (no longer crispy on the edges if it's been sitting there a while, but otherwise quite good) and the big meat and vegetable buns (very good. I love giant buns, and the fillings are flavorful, plentiful, and not at all sketchy tasting/feeling). It's great fast food. I've also run in an grabbed bakery items before/after a DTF run many times, and they have always been good, if not particularly memorable. In case it's not obvious, they also serve hot and cold drinks, including boba drinks. The one time I got a boba tea it was perfectly fine.