I wouldn't be surprised to hear something such as "Where can I get/grab a shower", for example, but I do think using a verb other than 'have' or 'take' is much more the exception than the rule.
On the other hand, saying something such as "Where can I find a shower" is perfectly OK. However, in this case, the question is much more about the location of a particular type of facility, and less a question about where a particular activity can take place.
Finally, 'get' might be more typical in this sort of structure (with 'shower' used as a verb):
- I woke up so late that I didn't have time to get showered before I left the house.