Do Sims ever go places other than home and work?
Sims will never be anyplace other than home or work by their own free will, however, you can send them shopping or relaxing (spending money in the process).
The most likely reason for why they do not go places other than home or work on their own would be because doing so would cost money, which a Sim cannot manage without the player's prior consent.
Note that this answer only covers the base game of The Sims 3, and does not cover any expansions.