If you're interested in the historic center of Lima, the Balcon Dorado would be a good, moderately-priced place to stay. It is a safe, independent hotel managed personally by its friendly, helpful owners. It is situated in a grand old nineteenthy-century building, the Eiffel Mansion (the Paris tower fellow); the rooms are large and clean, with high ceilings, good beds, nice furnishings.
The location is excellent: only one block from the beautiful Plaza Mayor, the center of historic Lima. Apart from breakfast, which the hotel provides, your dining can be taken in any of several cafes and restaurants of all types within a quick walking distance of the hotel.
Admittedly the hotel is a bit difficult to spot from the street -- just a small "Maison Eiffel - Talleres de Arte" sign beside the entrance. But you probably won't have to go hunting around for it, for the hotel provides airport pick-up on request. (They charge the current taxi fare, but it's stll nice to have the car waiting for you when you arrive -- as anyone knows who has flown into Lima.)
The owners also manage an art gallery in the same building, which can make for a unique stay. Finally, note that traffic can be loud throughout Lima's historic center; you may want to request a room that doesn't give onto the street.