When is the best time to take doxazosin to reduce having to get up in the night?

No specific time of the day

Doxazosin is used to treat hypertension (high blood pressure), or to improve urination in men with benign prostatic hyperplasia (enlarged prostate).

What are you taking it for?
If you are taking it for an enlarged prostate this is the most likely the cause of your interrupted nights. Not the doxazosin.

Unless you are taking a controlled release (long acting) formulation it does not matter what time of day you take the medicine. Whatever works best for you. It is a good idea though, to take it at the same time of day.
The controlled release tablet is best taken in the morning with breakfast.