I'm newly car-free, and also recently moved from a lovely place in the country (where, like Chicky2, we could easily be busy all day without leaving, and which was also just close enough we could bike into town if we really, really wanted to) to a big city that is not only not walking-friendly, but is also very, very hot in the summer (100+ during the day and 90s at night July-Sept). So it's actually dangerous to try walking very far with the kids. So right now, during the day, we go nowhere until dh comes home from work. Late afternoons, once the sun is not overhead, we can stand it outside for a bit.
We do all have bikes, but people drive like they either want to die or kill someone, so I don't even want to put the kids on their bikes. I am waiting for school to begin in September before venturing out (my kids are school-aged) on my bike and by foot. I can get a cab, but I'll go broke if I make a habit of that. Meantime, it's Ramadan and we're fasting, so we're indoors, anyway.
The kids have been passing the time reading, doing review workbooks, and playing a lot of games--Internet, board games, chess. They draw and paint, build bedroom forts, play with our cats. We clean house all together and they help me prep the table for breaking fast in the evening. Evenings, I just started going out to jog/walk, and we can also swim in the compound pool, and go out to various parts of the city to walk and check out shops and such--which, as a PP mentioned, means we spend money.
I don't know anyone here yet, either, so it's not like we have play dates to make or parties to attend. It's been a rough summer, and I can't wait for school to start in another month.
Once the weather cools off, the kids and I will easily be able to walk to the beach, and we have two great parks and a public library also all within walking distance. Even a mall is not too far away for walking in non-dangerous weather (let's say below 90 for the kids). And starting next year, I will spend summers back in the US, so this is (I hope) a one-time challenge for us.
A long time ago, when ds was 3-4 and dd was a baby, we lived in a lovely small town and even though I had a car, I spent the good-weather months being as car-free as possible. I had a bike and trailer, and we went all over town in it. Helped me lose a lot of weight, and save our family a lot of money, too. Those were a couple of wonderful summers.