Is there any place where I can take a shower at Guilin airport?

Well, as I know, no shower facility is inside the terminal building. According to the length of your stopover, you can just find a hotel nearby the hotel. Then take a shower and take some rest. Airport Hotel is about 450 yards (400 meters) away from the terminal building. The fare is CNY 250 to 300 per night. It provides clean environment and kind service. You can go and see.

Thank you for your answer. I have another question.
Can I check-in anytime without booking?
Thank you.

Yes, you don't need to book the rooms in advance. Just arrive at the hotel and check in on that day. :-)