New Street doesn't appear to exist now, but it can be seen in the lower right corner of this 18th century map: http://www.motco.com/Map/81002/SeriesSearchPlat...
The overlays that highlight 17th century London features are approximate and derived from:
Open location in Google Maps: 51.515652, -0.106878
wisteria53 • Link
A remnant of New Street is still there, but it is now called "Little New Street":
Chart showing the number of references in each month of the diary’s entries.