The artisan markets along Av. La Marina are less touristy than the markets in Miraflores and less convenient located. Anyhow even if the area suffered from the growing markets in Miraflores you can still find the one or other "mercado" selling a good variety of handicrafts from all over Peru.
The two bigger markets are Tesoros del Inka on Av. La Marina block 7 and the Gran Mercado Inka on block 8. Check out also adjoining Av. Sucre.
When taking your time you surely find some treasures bringing back home from your trip. Prices at the markets in Pueblo Libre seem to be a little bit lower than in Miraflores, but still bargaining is a must!