Searching google for something related to a slope in Tokyo and Kiyomasa, gave the result of Shikyonanji Zaka at Ikegami Honmon-Ji.
When you enter the temple from the Somon Gate, you will see stone steps is called Shikyonanji Zaka. It is said that this slope with its 96 steps was dedicated by Kiyomasa Kato during the Keicho age (1596 to 1615 during the Edo period). While going up these steps, why not stop and look back at the beautiful scenery unfolding behind you.
And this Shikyonanji Slope does evoke a certain element of a dreadful name, only not the kind the DB were probably thinking of. It translates to: Difficulty-of-maintaining-faith Slope.
The problem with this solution is that I'm kinda projecting, and in Japanese, this name might not sound that dreadful. Plus, there's still the issue of the numbers 7 and 3 that aren't really resolved here.
Speaking of which, with the mention of a spear and the number 7, it's very likely it's a reference to the Seven Spears of Shizugatake, which Kiyomasa was part of. There's another reference in Kiyomasa's life that relates to the number 7, I.E. the Seven Year War, but considering the mention of a spear, it's more likely the Seven Spears is part of the solution.
All of the above considered, whatever the location is, it should be close, because even if they solve the case, there's still over an hour drive back to Yamanashi. I'm pretty sure Gosho brought up a little Chekhov's Gun - the patrol car. After the case is over, Yumi or whoever will probably drive Shuukichi back to Yamanashi in the police car, so they could speed back before the time is up (unless Shuukichi gives up on the match, of course).
Dunno if the culprit's mentioned shogi tiles are of any importance, but maybe later I'll write more about it. Regardless, both Shuukichi and the culprit mentioned an incident from 10 years ago, and Shuukichi said the match he had left a bitter aftertaste, so I'd say it's probably related.