Before I arrived, my parents were very worried about my safety in the city while traveling around. And for good reason. At the same time, how one travels around a city can vastly change how they experience said city. Driving through New York City, for instance, is very different from taking the subway or the bus.
My favorite way to explore a new city, or even one I know well, is to walk! Of course, some cities are more walkable than others and sometimes the weather can deter you. Plus, depending on when you're out, it can also involve a lot of "street smarts." But by walking around, you can get a sense for the people, the architecture, etc. I think it's the best way to learn your way around; you learn street names and street layouts much more quickly, you are better able to find your way when/if you get lost, etc. Plus, you can stumble upon restaurants, shops, and coffee shops (if you're a coffee person) to try or to jot down for a future day. You get to experience different neighborhoods, and you'll see a wide range of different people.
Whatever it's called in a given city, if there's a subway system, I always try to take advantage of it when I'm unable to walk. Some systems are better than others. The NYC subway is extremely extensive and is just something everyone should experience; it's such a vital part of the NYC experience and our lifestyle. Taipei's MRT system is very small in comparison but is extremely clean and efficient. The metros in São Paulo and Buenos Aires are much older, most don't have AC, and you better keep an eye on your possessions. Subway systems are also great ways to learn a city's layout. Taking the metro in Barcelona definitely helped me somewhat with directions and sense of place within the city.
Far from my favorite mode of transportation, buses can be the most extensive transportation systems. I personally think of them as being mostly a local mode of transportation, simply because it often requires much greater knowledge of a place, or at least all those bus stops. I feel that they tend to be the most full of locals of all kinds, although depending on the city it may be more of the middle/lower class. Whenever I successfully take a bus or learn a bus system, I feel so much closer to being a local or having a local's experience.
For travels entailing longer distances, trains are great! I often take the train home during the school year. I took an 11-hour train ride to Montreal once. I took the train to Figueres while in Barcelona. I took the train in and out of Taipei when I was studying in Taiwan this past summer. Trains can be great modes of travel depending on where you are, but they aren't always the most efficient forms of travel (11-hour train ride to Montreal vs. 2 or 3 hour flight...). One day when I go to Europe, I'll definitely travel around more by train, though!
Of course, airplanes are great for all different types of travels. Depending on where you're going, they can also be the most time efficient methods of travel. And depending on the airline, season, and location, they can also be very cost efficient. I've yet to travel around much by plane, but I could see it being helpful in Europe (where trains aren't as efficient) and South America. (I can't speak for other locations, as I'm not as knowledgeable about transportation there.)
Trams, Gondolas, Etc.
These are always fun and unique ways to travel. Trams tend to be historic, while gondolas and such can be helpful in quickly getting to the top of hills and mountains and such. They offer great views and are totally fun!
I get sea-sick, so this isn't my preferred method of travel, but there are some great reasons to take a boat/ferry. The Staten Island Ferry currently offers a great, free view of the Statue of Liberty. Taking the ferry from Buenos Aires to Uruguay is the best way to get there. And you can sometimes get lovely views of a city's sky/coastline!
Also a not-very-preferred method is to travel by car. It can sometimes be really necessary to get to places. It can also be the most convenient or cost efficient, especially if you can drive with others and split gas costs. That said, you also have to deal with traffic, car-sickness (if you're like me), road rage (yours or others'), local driving laws, figuring out highway systems, etc. I personally also don't drive on highways yet and/or often don't have access to a car when I'm abroad/away, so that doesn't help much. But it's very helpful in, for example, getting to mountains or to places far from public transport. And sometimes it's just nice being able to travel around without relying on others. Plus, who doesn't want to take a road trip at least once in their life? I can't wait for the day I can do a cross-country road trip with my friends! West Coast, here I come!
Flying Ford Anglia, the TARDIS, the Hogwarts Express, Millennium Falcon, etc.
Okay, okay, you might be a bit confused. I know, these aren't real methods of travel. But imagine if they were?! I would love to be able to travel around with the Flying Ford Anglia. You could use a car without having to deal with most of the hassles of driving (maybe just parking). As long as you're smarter about it than Ron and Harry, you could get around without anyone seeing, you can fly over beautiful scenery, and it'd probably be close to teleporting. It'd be like flying on an airplane but without being so environmentally harmful (probably). And it'd make a future road trip so much easier! My friends wouldn't have to deal with me needing to sleep in the car because I'd get car-sick otherwise. Just don't crash into the Whomping Willow ;)
Similarly, I'd love to travel on the Hogwarts Express. Of the fantasy methods above, it's probably the least flexible. But that scenery! I would honestly just love to sit in one of the cars with some friends. It sounds nice for a medium-length journey. And, I mean, who wouldn't want to ride the Hogwarts Express?
And then there's the TARDIS and the Millennium Falcon, which are actually somewhat similar. With the TARDIS, I'd be able to travel through space and time...how awesome does that sound?! Plus, if you're ever attacked, you would be protected. The TARDIS can also help translate languages! It's essentially like teleporting. You could go anywhere, at any time, almost instantly. It'd make travel so easy. Just take out all the dangers that come with traveling with the Doctor, or just steal it from him, and you're all set. ;) The Millennium Falcon is much larger and unwieldy, but you can jump to light speed and travel to galaxies far, far away. Plus, it has so much history and is such a classic Star Wars vehicle.
While these aforementioned methods of travel may not be possible, you can rent an awesome car for your next trip through Turo. You can take the infamous Aviato Escape from Silicon Valley or the Wagon Queen Family Truckster from National Lampoon's Vacation for a spin. They have all types of cars and can make those road trips and adventures a little easier! They're a great new car-rental option that you should definitely look into the next time you're in need of a vehicle.