A Hasselblad 500 series is a great camera with a great lens, but it is a clunky, slow camera. I use mine almost exclusively on a tripod. The Hasselblad SWC, however, is great for street shooting, and the 38mm Biogon is a mind blowing wide angle lens. It's my favorite camera. Look at the SWC group on Flickr.
If you want a "normal" lens for the street, look at Mamiya 6, 7 or 7ii rangefinders. All have really great optics and will not seem too much different from your Leicas. Don't discount old 120 Zeiss, Voigtlander and other German folders. They mostly have 4 element Tessar style lenses, but are not as rigid and precise or as fast as modern rangefinders. But where else can you get a 6x9 image for a couple of hundred bucks?
Finally, as others here have suggested, TLRs, with a style adaptation, can be used on the street. Rolleiflexes sport either Zeiss Planar lenses, like the Hassy, or Tessars (or the Schneider counterparts to those lenses). YashicaMats have Tessar knockoffs that are very sharp from about f8 up. I have not used Mamiya TLRS, but lots of folks do, and they even have interchangeable lenses and a bellows.
Lots of options at lots of price points out there for medium format, and you'll be blown away at the quality of those big negs or slides. Have fun.