I would advocate using Tri-X @ ISO 400 for daytime street photography, developed in D-76 1:1. This works very well for me - no issues or complaints.
If you need more speed than ISO 400, Tri -X pushed to ISO 1600 and developed at ISO 1600 looks really nice - to my eye, at least. Straight work prints at 8"x10" size show nice smooth grain with a bit of a loss in contrast - noticeable but not objectionable. The contrast loss can be addressed in printing.
If you want finer grain than Tri-X, give Fuji Acros ISO 100 a test drive. Acros is not as forgiving as Tri-X is, though.