What's a 1K doing on a MR to Lima?
I was in Lima for a wedding earlier this year. I don't know the city that well, but these are my general impressions.
Taxis are easy to get from the airport and cost about $20 IIRC to most downtown areas. The neighborhoods I was in (mentioned below) felt completely safe.
Your hotel is near the old center of the city. I would spend the morning/middle of the day exploring that part, and the afternoon/evening in San Isidro/Miraflores (residential areas). Check out a map for a location of all 3 neighborhoods: they kind of lie in a line, with Miraflores near the ocean, the old downtown farther inland, and San Isidro lying between the two.
The best ceviche I've ever had was at Punta Sal. There are two of them, one in San Isidro and one in Miraflores.