[QUOTE For some strange reason without a car a backpack and Baby Björn carrier seem to be enough.[/QUOTE]
Congratulations! We have a two year old daughter and have managed very well without a car in England and now in Zurich. And yes, the less space you have the less you carry with you! Also think about investing in a really good baby carrier, like an Ergo. It's fantastic for just walking around and for getting on and off public transport. It's also great for hiking.
Cars, who needs them?!