I have yet to see my Sims go anywhere or do anything other than things around the house or leave for work. I would expect that, based on their personality traits, they would do things. At the very least, I'd expect them to go to venues in their city. Or even more, use their attributes and plan a vacation. Are these tasks too complex for Sims, even with story progression and free will?
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.