I had to go to Europe last month, so I decided to wander around a couple of cities of various population densities during my downtime.
A considerable amount of the paved roads had dedicated bike lanes (especially in Ireland and the UK), and the typical cyclists who chose instead to bike on the car lanes. Cycling lanes tended to be more present in larger cities. As expected, parking is expensive and a bitch to find, especially in the city centers. Roads tended to be more narrow, and highways usually were around 2-3 lanes per direction. I mainly attribute this to the small sizes of European countries in general in addition to less urban sprawl being present.
Excluding tourist buses, intracity transportation tended [more often than not] to be fairly inexpensive, clean, frequent, and prompt. Depending on what country you go to, there might be trams and rentable bikes in addition to the usual buses and trains. Ride-sharing isn't as prevalent, but taxis are fairly present. Intercity transportation mostly suffers from the same problems as in America, wherein it comes less much often and is fairly pricey. Ireland has a network that spans across the island country and covers a great deal of intercity travel, although I will note that cars are still favored in that regard. Depending on location and if your car runs on diesel or petrol, gas prices are approximately 1.6-1.9 Euro/liter, which translates to over $6 USD/gallon.
Buildings tend to be small and clustered together. There is a high emphasis on walk-ability in some cites (again, mostly in the busier cities). There are car-free roads (which your GPS will still try to steer you towards because they're wide enough for opposing car traffic), but they appear to be limited in general to marketplace streets or near the city center. While there are a lot of food shops where you can get groceries, most of them do not have shopping carts. I presume it's due to the fact that since there is less of an emphasis on car transportation, that it would mean that people would shop frequently at those stores, but pick up only a few items each time. I rarely saw people with those personal grocery carts, though.
Despite what the /r/fuckcars people think and have done, Europeans in walkable cities do not, in fact, drag large appliances on public transportation after purchase. They do not appreciate the idea of other people doing it and fucking up everyone else's commute. They behave like normal people and ask to rent a box truck to bring it home, or request the company deliver it to their house.
That being said, can walkable cities exist in the US? I'd say it depends on the city, with very small cities being more likely and easier to do. You'd have to account for the several hundred billion it would take to knock down existing buildings, relocate businesses and people, and reshape aging infrastructure for larger-scale projects. The huge price tag seems to be an idealized vision, given the amount of grift and political incompetence the US has (see: the failed California high-speed train, and NYC MTA workers giving themselves several hundred thousand $$ bonuses). Ireland's sq mileage is slightly smaller than North Carolina, with Arkansas' population (~5 million), so it's no wonder that Ireland has enough land to use for various public transport.