The city is divided into several quarters. You can walk within each quarter, but between quarters you need a bus or taxi.
It is helpful to have a general overview of the quarters most important to tourists:
Centro in the north, just south of the Rimac river, has the central squares, Plaza Mayor Plaza de Arma and Plaza San Martin, churches, colonial architecture, the presidential palace and Congress, and shopping streets.
To the south-west is Pueblo libre with the two main museums, Antropological and Larco Herrera.
Further south is Miraflores, an upscale touristy neighborhood with restaurants, nightlife, and hotels
Further south still Barranco, a bohemian beach-side neighborhood known for its nightlife.
By taxi
If going further, a taxi ride between adjacent neighborhoods costs about US$2 6 soles, if you speak Spanish well enough. A longer ride may cost from US$3-7. A reasonable price for a taxi service between the airport and Miraflores is about US$12 35 soles, but may cost more from within the airport. By custom, taxis do not have meters; rather, the fare should be negotiated before boarding the taxi, or, if you request one by phone, at booking time. If asking for a ride on the street, don't be fooled into getting into the cab before a rate is negotiated. Be also very discerning about which taxi you choose, and avoid hailing random cabs off the street as much as possible.
Caution is advised in Lima, and the same goes for taxis. As a foreigner, do not ever get into shared taxis, and it might not hurt to look if there's someone hiding on the back seat or the trunk before entering.