The city centre is compact enough to walk. Most sights of interest — the central parks, the cathedral, the markets — are within fifteen minutes on foot from the main plaza.
Taxis are plentiful and cheap by Ecuadorian standards. For the outlying attractions like the Atocha-La Liria botanical garden and the Martínez-Holguín house museum to the north, a taxi is the most practical option. Agree on a fare before getting in.
City buses run frequently to most neighbourhoods but are crowded during rush hours and not well-signed for visitors. Taxis are the easier option for getting around if you are unfamiliar with the city.