New York City
In New York City, pay close attention to alternate-side parking (and be prepared to fight for a new space against experienced veterans), but also remember that politicians have found it beneficial to keep adding holidays for the unpopular rules (there are now 43), so feel free to relax on, say, Ash Wednesday, Purim, or any of the three days of Idl-Adha.
As for Boston, we'd advise you not to try to park at all, but that would mean spending all your time driving, which is arguably worse. You could take public transportation, but the T goes nowhere and the buses have all long since vanished into the Big Dig. If you must visit, bring good walking shoes, or a Segway.
Parking in Chicago is a breeze, as long as you aren't trying to park downtown, near an attraction or event, or anywhere on the lake side of Broadway, or anywhere else after five, and, ideally, you're visiting a friend with an extra parking place who lives right on the El. Also, watch out on election day, as spaces that look empty might be occupied be the spirits of the dead, who rise biannually to vote.
In L.A., watch out for the unposted overnight parking restrictions in Beverly Hills. (Non-residents pay steep fines for leaving their cars near celebrities.) Also, some of the fancier hotels offer free parking to their bar patrons, so if you don't mind paying $100 for a cocktail and reading your waiter's screenplay, you can avoid the hassle of the street.
Visitors to Houston might be surprised by its public transportation system (that is, that is has one at all). This largest of American cities (bigger in square miles than the state of Israel) has a single Metrorail running from one unplanned knot of sprawl to just within inconvenient walking distance of the middle of nowhere. The short story: bring a car, park at one of their twenty-seven Applebee's.
Getting around in Seattle is safe and easy, thanks to the city's commitment to establishing bike lanes and racks and--wait, you weren't talking about bicycles? What are you doing in Seattle, anyway?
Before parking in Miami it is imperative to visit a dramatically lit, faintly sepia-toned crime scene. Take many sensationalized grainy close-up shots of the carnage while a theramin is played badly in the background, then look into the camera and say something nonsensical in a gravelly voice that makes it seem profound, like, "I guess she finally fed the meter." After that, if anyone tries to give you a ticket, loudly remind them how tough the streets are and how you can't afford to play by the rules.