So first, let's start with the opening theme...
In that scene, which is also the first image on this web page (see above), we see an elevated train station and a yellow sign on the building on the left that says "EVELT LIQUORS". "Evelt" is probably the word "Roosevelt" cut off, meaning this has to be somewhere along the number 7 subway line, which travels along Roosevelt Ave. Also, looking carefully, we see that one of the tracks is actually one level above the station. The only place this happens is at the 111th St stop on the 7 train. Turns out 111th is a one-way street heading north, so the shot is actually looking south at 111th St towards Roosevelt Ave, in Corona.
Below is a photo of the actual location:
Railroad overpasses that look like that usually mean Long Island Railroad, and based on the traffic and post-war buildings, this is probably a more developed neighborhood in western Queens. Communities that fit this bill and have the LIRR passing through are Elmhurst, Corona, Rego Park, Forest Hills, etc. My initial thoughts were this is either Broadway or 63rd Drive near the LIRR overpass. So, after trying both places in Google Maps Street View and looking for a white colonial looking church, the answer is...
Broadway. This spot is right outside the Elmhurst Ave subway stop on the M and R trains. The shot is looking southeast towards the LIRR Port Washington Branch (now that I think about it, the overpass is too skinny to be the four-track main line over 63rd Drive). The Reformed Church of Newtown is the name of the church in the background.
Interesting fact... the intro from the earlier seasons initially showed lower Manhattan, but was replaced with Elmhurst after 9/11.
Below is a photo of the place:
Here is a photo of the the park:
From 0:13 to 0:16 Carrie and Arthur are shown in different playgrounds and parks. Unfortunately, I just don't see enough here to be able to figure out where they are. If anyone does know, feel free to tell us in the Comment section below.
The fact that the train is a redbird and that the el is metallic means that this is somewhere along the 7 line over Roosevelt Ave. That giant structure could be Shea stadium (the series was filmed before Citi Field). But then again, the fact that there are so many parallel-parked cars suggest that this is a developed commercial or residential neighborhood, ruling out Shea (the stadium was surrounded by Flushing Meadows park and a giant parking lot).
The only other structure so big near Roosevelt Ave is Elmhurst hospital. Looking around that area in Google maps, I actually found one street that doesn't go straight through Roosevelt!
Here is the photo of 78th looking south. That giant structure is the parking garage for Elmhurst hospital. Looks like Champion Ping Pong is no longer there...
0:20 is under an elevated train; looks an awful lot like Roosevelt Ave. If you check the street sign in the image on the left carefully, you can see that it starts with the number 8, meaning this is somewhere along Roosevelt Ave in the 80s. (Maybe they drove down 78th St in the previous scene, filmed, made a left on Roosevelt, and filmed again).
There's a lot of pre-war apartment buildings in this shot, which could mean Jackson Heights, Astoria, Forest Hills, Woodside, Sunnyside or Kew Gardens.
To be honest, this one took me a while to figure out because I kept going up and down 37th Ave (which is a commercial street in Jackson Heights with lots of pre-wars) in Street View, yet the buildings never matched up exactly. Between this and Kew Gardens, I was ready to give up, but decided to give Austin St in Forest Hills one last try.
Sure enough, this is Austin St looking southeast towards Ascan Ave. Below is a photo of the place. You can see the big building with the water tower in the background.
But believe it or not, I stumbled upon this one by absolute chance. I was looking for something else and noticed that this was a block away.
The houses are on the north side of Penelope Ave between Woodhaven Blvd and 84th Pl in Middle Village.
Last, but not least, we have the Lemon Ice King of Corona at 0:25. You can find it at 108th St and Corona Ave.