The LP Columbus Hotel is right next to the Hernando Siles Olympic Stadium. The area is going through some renovations, including the Tikwanu Plaza, a recreation of an indigenous archeological site. There are plenty of shops and restaurants and the hotel is about a 10 minute walk to one of the Cable Car Stations. If walking is your thing, then the hotel is a 12 minute walk to Plaza Murrillo, the actual center of La Paz and all of Bolivia. The Presidential Palace and the Cathedral are located there.
The hotel is clean, safe and modern. The employees are a very friendly and helpful. Talking about safety, La Paz is one of the safest cities in South America.