Great thing about Lima is everything is delicious apart from KFC in Av Comandante Espinar.
Westin is in San Isidro right? I think...
I'd go to Vivaldi
http://www.vivaldi.com.pe/
For a nice bar with arty farty light bites you might be interested in Bravo Restobar.
http://www.bravorestobar.com/index1.html The chef is very well respected
I think they are both tripping distance from your hotel
You really have to try pan con chicharrón and camote and pickeld onions. Its the best sandwich ever. Nicest one I had was out of a cart in Surquillos, this place
http://www.travbuddy.com/Glotons-v359372 does them 24/7