I'm genuinely curious: Here in germany we have car-sharing offers that allow you to pick up a car on the street, ride it to where you want to go and then leave it parked there in the larger cities. The fee is usually about half of the fee of a cab. Then there's the same for bicycles. The combination of public transport and car-sharing in berlin is awesome, at least in the city center: I go most ways by public transport and then grab a car or bike if I need to. If I really need to travel long distance by car, I get a rental and I'm coming out ahead financially, even if I throw in the occasional taxi ride because it's late and I'm lazy. From the posts here I get the impression that this doesn't exist in the US - and I can't imagine that.
A handful of cities in the US have in the last few years gotten a service called car2go, which is exactly what you describe. It's not available in the biggest cities, though. A few cities are also starting to have bicycle-sharing services. It's just not very common, yet.
We have it in Toronto and it's super useful sometimes to quickly get somewhere within the downtown when transit would be slower and cabs more expensive.
