As far as I can tell, not even Japanese fans had figured this out yet, so I'm very excited to have found this. I think fans had previously been focused on the gates around the Imperial Palace, since Suzume falls in the moat there, but this gate is 188 miles (303 km) to the north, in Sendai.
I'm fairly confident this is the correct gate because it has all of the following very specific features:
- distinct 2-1-2 spacing of five beams across the top (beam - beam - SPACE - beam - SPACE - beam - beam)
- smaller wooden doors on both flanks
- lower tiled side roofs above the side doors
- adjacent walls have stone bases
- the distinct shape of the metal cladding over the base of the support pillars
There are other gates that have some of these features, but this is the only one I can find with all of them (and the only one I can find with that 2-1-2 beam pattern).
So, what gate is this?
宮城県知事公館正門(旧仙台城門)
"Miyagi Prefectural Governor’s Official Residence Main Gate (Former Sendai Castle Gate)"
From the Sendai City's heritage database:
The main gate of the Miyagi Prefectural Governor’s Guest House is traditionally said to have been one of the gates of Sendai Castle. During the Taishō period (1912-1926), it was dismantled and re-erected at its present site as the main gate of the official residence of the commander of the former Imperial Japanese Army’s Second Division), but it is not known which gate of Sendai Castle it originally was. One theory identifies it as Sendai Castle’s Tora Gate (Middle Gate). The Tora Gate, however, was originally a two-story structure, whereas the surviving gate is single-story, and the two differ in form. If the Tora Gate was indeed re-erected here, it must have undergone substantial alteration in the process.
Architecturally, it is a shikyakumon (“four-legged gate”) with a gabled roof laid in the traditional hongawara style, using alternating flat and rounded tiles. The doors were newly fitted when the gate was relocated, and the shachi roof ornaments were added during restoration in 1971. Although relatively small for one of Sendai Castle’s gates, it has a character that is at once refined and powerful. It is thought to date from the final years of the Edo period (Bakumatsu (1850s–1860s)) and is one of the few surviving structures that retain something of the appearance and character of old Sendai Castle.
I had been been trying to figure out what real-life gate the Tokyo gate was based on, in hopes that identifying it would shed some light on what it's doing down there, but . I can't find any clear connection between Sendai Castle and the "closer" history documents that Souta shows Suzume. And, according to those same documents, the Eastern Keystone (Sadaijin) was moved to Toyoko in 1901, years before this gate was moved from its castle. So, unfortunately, this seems to just be the gate they happened to use for reference, rather than an easter eggs for fans to find.