When I travel in cities I always ditch my car and take public transportation. If you park in the outskirts of the city you can almost always find park that's both safe and super cheap (or free!) for several days. If you park somewhere on the outskirts of the city you can usually find a safe spot to leave your car and it's almost always free.
Not all cities are alike, though. Every city has their own system of public transportation and method for paying for it. Whenever I think about visiting a city, the first thing I research is their public transportation system. It often reflects the quality of the city and how easy it can be to explore.
My Travel Partner and I had the best time in Chicago because of their amazing public transportation. Most cities usually don't have such widespread coverage within their city but we could always walk to anywhere we wanted to directly from the L-train without having to make a bus transfer. It was a lot cheaper than most cities since we were able to buy a weekly pass for a very reasonable price, although it definitely wasn't the cheapest city.
There are other cities out there that aren't so nice, though. San Francisco is by far the worst I've seen. They charge you based on the distance you travel on their BART system and everywhere else is 2 bucks per ride! That may be reasonable for people visiting for a few days but any longer than that and the costs add up, especially if you plan on exploring beyond their limited routes. I can tell you as a person that's lived in the Bay Area before, it's even worse if you live there.
Overall, though, cities have some pretty amazing public transportation systems. It's a great way to get a feel for the culture of the city and the overall outlook of the people. I've often found that the best way to see how friendly the people there are is to “accidentally” bump in to them and see how they react.