From the Quito airport to the majestic Old town of Quito you are looking at 1 hour to one hour and a half travel time. Taxis from the airport should charge around $20-25 no more.
We can help arrange a taxi upon request 24 hours a day fro here at the hotel near the airport in Quito.
You could also get to the old town by bus by getting on the green city buses that leave from the airport. Get one going to the station in the north of town called RIO COCA. ($2)
Once in Rio Coca catch the tram ECOVIA south to the old town.
Total cost ($2.25 each way)