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I've made it to Ust Natha for the first time, and I've looked ahead just enough to know that there is an involved sidequest that will open up later concerning a certain tower. I'd like to tackle it at some point, but I'd also like to take my time while doing so. But since entering this city, it seems like I'm always on the clock with time limits for the main quests in front of me.

Here's the question: Is there a point during the Ust Natha sequence when you're *not* on the clock? Perhaps somewhere down the stretch when eggs are involved?
You have plenty of time to do whatever you wish, provided you are not the kind of player who rests between every fight. When you are directed that you have 12 hours or 3 days, that's plenty of time to do whatever you wish. You only need to be mindful that you are in a potentially hostile city and so should take directions seriously.