The below were highlights of the 2 days I spent in Lima in 2009. I am afraid I don't have specific restaurant recommendations but I did enjoy the food there, plenty of good options.
The Museo Larco (full name Museo Arqueologico Rafael Larco Herrera) which is such an outstanding ceramics museum, in a country with such a long history of artistry in this area, that I would highly recommend it to everyone, I think even those who usually only have a passing interest in art museums would really enjoy it.
The National Museum (Museo de la Nacion) - I would go specifically for the floor devoted to the history of the Shining Path movement, which dominates Peru's contemporary history
The Western adjacent neighborhoods of Miraflores and Barranco, which overlook the Pacific coast, are good neighborhoods to wander, look at galleries and shops, etc. There are excellent restaurants as well. They are upscale residential neighborhoods so not a place for bargains, but there are some beautiful things.
The historic center surrounding the Plaza de Armas is the area where you will find the old colonial city. I am sure you could organize a tour through any hotel but every guidebook will also include a self guided walking tour and the area is compact, the Cathedral was a highlight.
The Parque de la Reserva otherwise known as the Magical Circuits of Water Public Park in Lima IS NOT to be missed! Have you ever seen the Dancing Fountains at the Bellagio in Las Vegas? This is that on Steriods. Its a huge city park that has several large fountains throughout it. It only costs about a $1.50 USD. Some of the fountains are interactive that you can play in or walk thru. Now the main fountain has three shows a night Wed-Sun. Here is where the "dancing" fountains are. In the center they shoot water straight up and shoot lazers like a rear projection screen. The lazers help animate dancers and other neat graphics choreographed to music. The show runs about 40 minutes. It is considered the largest public fountain complex in world by Guinness Book of World Records. I could of spent my whole evening here I enjoyed it so much.
Lima has 40+ distinct districts. I HIGHLY recommend you stay in the Miraflores Area. It is safe and pleasant there and along the coast. They have this awesome shopping center called the Larcomar which is imbedded INSIDE a cliff...its pretty neat to see. Lots of familiar places like Starbucks and Chilis but also some Peruvian restaurants such at Tanta. The tour bus company Turibus has an office there and all their tours start from this location. The tours unfortunately were mediocre because the commentary was pretty sub-par. I highly recommend staying at Hotel Ibis which 1.5 blocks away or so and trying Pisco Sour, the national drink of Peru at Tanta's :)
These are both of my travel stories from Lima. Please kudos them if you found this information helpful :)