I live in San Francisco with my husband, a 6 month old baby, and a cat in a one bedroom apartment near the beach. We have no car but don't need one since the public transportation system in this city takes us where we NEED to go (not always where we WANT to go.)
When we need groceries, we walk about 1/2 mile to Safeway or a just few blocks to a small organic co-op market. We have a shopping cart with wheels and a telescoping handle (similar to a wheeled suicase but it's open on top and constructed of mesh instead of thick material) and we take this with us when we need to get heavier things. I walked to the store with this cart through my entire pregnancy and now I put the baby in a carrier or sling and walk, pulling the cart behind me full of groceries. The walk takes about 20 minutes, it's a scenic path along Highway 1 near the ocean, and it's good exercise!
In addition to walking wherever we can, we frequently ride buses and streetcars with our baby. We even took the streetcar to the hospital when I went into labor! Not only is riding transit less stressful than highway traffic, you really get more exposure to different types of people in your community (some admittedly not so savory, but it's a good dose of reality nevertheless.)
I grew up in a spacious house in Texas and drove everywhere since the age of 15, but living carless now isn't as hard as I thought it would be. It saves gas money, insurance, prevents unnecessary shopping excursions to mega strip malls, curbs carbon emissions, etc... In some areas of the world it's much easier to be green, and San Francisco is one of those places. No heating bill, no air conditioning bill, no car bills.
Living in a small apartment (less than 600sf) also has surprising benefits, including avoiding unnecessary stuff that adds clutter. Efficiency, simplicity, diligent cleanliness, frugality...these things I've had to learn just to maintain sanity and a budget on one salary, but they've given me more peace in my life than I expected in return.