We will arrive late in the night to Guilin airport, at about 1.00 am.

Yes, it's easy to get to the downtown area at that time.
Well, what do you mean by city center? Take the Main Railway Station as an example, it usually costs CNY80-120 by taxi.

In addition, upon landing, you can also take the Airport Shuttle Bus to the city center, which usually stop at Civil Aviation Building at the cost of CNY20/person. The shuttle bus departs according to the arriving flights.