julietbat I was in exactly your position 3 years ago. We took the plunge and opted for a large house with very big garden, but on a country lane which means that even though the local shops, school and swimming pool are all within a 20 minute walk, we have to drive.
The road has a tight bend, and no pavement. I occasionally walk when I'm on my own, but when I'm with the DC I wouldn't risk it. It was definitely the down-side of the house and we thought long and hard about it before we bought.
Turns out, it's not really such a pain. There are lots of country paths we can take from our house, so going for long weekend walks straight from our front door isn't a problem (they just don't lead to the shops!). It is a bit of a pain getting the car out when I just want a pint of milk, but it doesn't happen very often.
Given that I'd have to get the car out anyway to take the DCs to school, it meant that I considered (and went for) a much better school outside our catchment area. That's worked out really well. Parking near the school hasn't been a problem. I leave 5 mins earlier than I need to, so always easily get a space, and the DCs have 5 mins more to run around the playground and chat to their friends before school. We make sure the DCs get plenty of exercise (dance / gymnastics classes, lots of time in the playground and countryside walks at weekends) to compensate for their lack of daily to-and-from school exercise.
The rising cost of petrol is an issue, but with the youngest DC about to start school I'll be able to take on more work, which will easily outweigh the extra. I just wish we'd had the foresight to buy a diesel rather than a petrol car before we moved.
Sorry for the long post. As you say, there's always going to be some kind of compromise, and for us, the house made up for not being able to walk. Plus, having the huge garden means that all their friends like to come here to play!