I stayed at http://www.lacomedie-lapaz.com/en/loge.htm for 3 nights earlier in the year.
It was quite central and the room came with a little kitchenette and fresh bread every morning, as well as a desktop computer and free wifi.
Not very easy for taxi drivers to find though, so worth taking a map before you leave. almost 6 years ago
As of late 2012, another standard boutique hotel inaugurated igniting a 1.3m investment. Like most boutique hotels, Stannum must have its charm, and it comes more less with a 100 USD stay per night.
However, you got other places which are inspired on the concept of boutique hotels
https://www.airbnb.com/s?location=la+paz++bolivia&checkin=&checkout=&guests=1 over 3 years ago