Downtown Lima has improved considerably since I was there before. The Plaza de Armas or Main Square has stunning colonial buildings, the main Cathedral (Catedral) and the huge Government Palace where you can see the daily changing of the guard late morning.
On the Plaza de Armas is the Basilica Catedral de Lima which has really stunning altars. It is worth the small entry fee when a mass is not being held. There is a small attached museum, the Cabildo Metropolitano de Lima or Museo de Arte Religioso which is a religious museum with vestments, paintings, manuscipts and other items. If you have time you might check out the Museo Palacio Arzobispal de Lima or Archbishop’s Palace Museum which can be included in your ticket to the Catedral at a higher cost.
In addition to the Catedral, make sure to visit the Iglesia de San Francisco, the Iglesia de Santo Domingo and Iglesia San Pedro. The Mercado Central or Central Market is a great place to visit and see the food stalls with fruits, vegetables and other food items. You will also find clothes, shoes, kitchenware, tableware, toys and books. It is near Chinatown and the Chinatown arch which is a popular spot with locals to eat and shop.
The colonial buildings are very attractive. Make sure to find as many wood balconies you can which date back to the Spanish Colonial period. There are purportedly more than 1600 in Lima.
Near downtown are two museums that you might add to your list. The first is MALI, The Lima Art Museum or Museo de Arte and the National Museum of Archaeology, Anthropology and History which was closed when I was there.