The street no longer exists, but can be seen at the bottom of this 1746 map.
The overlays that highlight 17th century London features are approximate and derived from Wenceslaus Hollar’s maps:
Open location in Google Maps: 51.515406, -0.103421
Fleet Lane runs left-right at center-bottom of this 1746 map
Not a "nice" area: between Old Seacoal Lane and Fleet Lane stood the Fleet Prison, a substantial stone erection built in the mid-12th century with a surrounding moat. Prior to 1641 it was a house of detention for crimes of any nature, but was subsequently used for debtors only.
Unlicensed marriages were performed by the Rector of St. James, until 1616 when he was suspended. The trade was taken up by clerical prisoners living within the Rules of the Fleet, and who, having neither cash, character, nor liberty to lose, became the ready instruments of vice, greed, extravagance, and libertinism. http://www.thebookofdays.com/months/july/24.htm
Prisoners of the Fleet did not have to live within the prison itself; they could take lodgings close to the prison so long as they paid the keeper to compensate him for loss of earnings. The area in which prisoners could exercise this privilege was known as the "Liberty of the Fleet" or the "Rules of the Fleet". The Liberty of the Fleet became known for its quickie weddings. Ministers (or those only claiming to be ministers) set up shop in taverns and houses. Couples wishing to marry in secrecy or in haste flocked to the area - many of them quite drunk and only briefly acquainted. http://www.okima.com/tour/fleet.html
Monday 25 July 1664:
"... and after dinner walked forth, and do what I could I could not keep myself from going through Fleet Lane, but had the sense of safety and honour not to go in, and the rather being a holiday I feared I might meet with some people that might know me. "
So I take it that Pepys didn't enter one of the establishments where he might have met one of the women available for such a 'marriage'.
Chart showing the number of references in each month of the diary’s entries.