The road can be seen starting at the top-right of this 18th century map, leading east along (presumably) the same course as the modern day Old Street. Today, the street leads slightly further along what, in the 18th century at least, was called Hoxton Road.
The overlays that highlight 17th century London features are approximate and derived from Wenceslaus Hollar’s maps:
Open location in Google Maps: 51.525340, -0.090401
Near the top of this map Old Street runs east off Rotton Row
[OLD] STREET runs W-E off the top of this map
At the bottom of this map [OLD] STREET runs past Old Street Square
Chart showing the number of references in each month of the diary’s entries.