Park Slope is consistently rated a top neighborhood in NYC. I have lived here since 1981 and raised my kids here. As far as describing how it "looks and feels," it is a historic neighborhood of 19th century brownstone and limestone townhouses. Much of it is a designated historic district. As far as "lawns," we do have front gardens, but I would not call them lawns, as the houses are attached, but set back a bit from the street. We have backyards as well. The zip code for Park Slope is 11215. It is a neighborhood within Brooklyn, so when you ask if there is a dominant architecture "throughout the city," Park Slope is not a city, but rather a neighborhood in the borough of Brooklyn, in the city of NYC. Apart from the townhouses, there are rental, co-op and condo buildings as well.
Here a New York Magazine article rating Park Slope as the top neighborhood in NYC: http://nymag.com/realestate/neighborhoods/2010/65374/index1.html
Halstead Property, LLC
Seeing that you are from San Francisco and having been to both areas I would say that park slope is similar to the area of Pacific Heights. Park Slope has many beautiful older-built & prewar townhouses and brownstones and it also has Prospect Park as a central focus and draw of the neighborhood. For a good visual representation of the neighborhood you can watch The Squid and the Whale which was filmed throughout the neighborhood.
Specific answers to your questions:
Do residents maintain their homes and lawns? - In general terms the answer is yes. Of course there are always divergent people but the majority of Park Slope is well maintained and consequently the property values are high.
Are there dramatic differences between different neighborhoods or zip codes? - Yes definitely! Park Slope is known for its brownstones and townhouses. See your next question for further elaboration on the answer.
Is there a dominant architecture throughout the city? - Relating specifically to architecture alone, the feel and character of a specific neighborhood may be resultant of the time it was developed and the architectural trends as well as the zoning restrictions or lack of them. Brooklyn Heights sits at the foot of the Brooklyn Bridge and was one of the first developed areas thanks to the existence of the bridge and the ability to do commerce with New York City. Brooklyn Heights is also known for its historic brownstones and townhouses. To better understand certain neighborhoods and their development I recommend you read Gotham which is the Pulitzer Prize winning history of the development of New York. It was co-authored by one of my dear landlords who is a professor and historian and lives in Park Slope.