There are three "top" restaurants in Lima that make all the lists. Central (tough to get a reservation, but good. They now only have a closed tasting menu now, so not as good as it used to be. Disappointing for most Limeños that I've talked to, but for a first timer, it might be a good choice. They offer ingredients from sea level to something like 4000 meters. Astrid and Gaston. Take a pass. Overated, and Maido. Maido is my hands down choice. We've recommended chefts to go there and they are blown away. La Lucha.. good, but nothing special. Pachita, good too, but a little touristy and I think you were trying to avoid that. I don´t know Mercado 28, but have heard good things.
Downtown? Look, there is a place right across the street from the Congress, on the second floor. The doorway is right on Abancay Av. but it is tough to spot. Closed on Sundays I think. Traditional food from the north of Peru. Try the Arroz con Pato, or the Cabrito (depending on the day). https://www.facebook.com/ElPaisanoFerrenafano/
The restaurant has two sections, but sit towards the street for a nice view of the Congress.
If you want to try Chifa, which is the Peruvian version of Chinese food, try the Salon Capon on Jiron Parruro 819, in China Town. Sit upstairs, not downstairs.
Fianally, I am not a fan of the food, but it is a really cool place to eat: L'Eau Vive (Ucayali 370). It's run by an order of French nuns.
Btw, downtown is good for lunch, not for supper.