You can get around the city by private car or jeepney. For visitors, the jeepney is an inexpensive option but traffic can be very bad, and since they're all privately owned, the drivers take forever to wait for passengers which is not too bad for foreigners, anything in a strange land is a new experience, even streetside life. And unless you take the front seat, doesn't offer much in terms of sightseeing.
Re taxis, try to go for the reputable ones Melvin, Light of Glory with radio facilities and phone call services, but if it's daytime, most of all taxi services should be fine.
