La Teoría de 6 Cafés, Calle Gral Mendiburu 890, Miraflores: They have cold brewed coffee as well (there is more caffeine in cold brew). Felix, the coffee roaster of Artidoro Rodriguez coffee (and grandson of Artidoro), may be biased as he is friends with the folks at this cafe (or did they become friends over a cup of coffee?). Note in the photo below that this cafe serves cold brew with orange juice along with other hipster coffee trends.
Milimétrica Espresso Bar, Av. la Paz 580, Miraflores: The link from Beanhunters provides lists of where to drink gourmet coffee around the world.
Colonia & Co, Av San Martin 131, Barranco: From the photos, it looks like they even have a real hipster with a manbun working here.
Caleta Dolsa, Av San Martin 223, Barranco (couldn’t find a link on the cafe so inside I include one of the area including a tip on a hotel to stay in): this place is only a few months old. It’s located in a sunken (basement) space.
And these two:
Neira Café Lab, Calle Enrique Palacios 1074, Miraflores: Also has lists of cafes, plus a notification about a foam competition.
Cafe Verde (this link includes even more coffee shops to try, though Aromia is gone), Av. Sta. Cruz 1305, Miraflores