Since the Mariscal Sucre airport is located in downtown Quito, and since there are really no good options right at the airport, I haven't included a section of hotels near the airport. The hotels in New Town and La Floresta are approximately 10 to 15 minutes from the airport, depending on traffic, while those in Old Town are some 20 to 25 minutes away.
In Old Town -- Quito's Old Town is in the midst of a major renaissance. Whereas just a couple of years ago I cautioned visitors from staying in this area, there are now several excellent hotel options in various price ranges, and the security situation has improved greatly. That said, you still need to be careful walking some of the streets around here at night, and taxis definitely should be used after nightfall.
La Posada Colonial (tel. 02/2280-282; posadacolonial@yahoo.com) is a good option in the inexpensive price range, just steps away from the Compañía de Jesus and Plaza de la Independencia.
La Floresta -- In addition to the Swissôtel, the Radisson Royal Quito (tel. 888/201-1718 in the U.S. and Canada, or 02/2233-333; www.radisson.com), at Cordero 444 and 12 de Octubre, is another dependable high-end choice in La Floresta.