I think you're thinking too narrowly -- some of the most popular neighborhoods in many cities are the very specific cultural ones (e.g. K-Town in LA, the Mission in SF, Chinatown in NYC, etc) where people from all backgrounds meet and mingle. You might go there with a few coworkers that are the same age/race/sex as you, but a big part of the reason that you don't stay on your block is for the diversity of experience. Rec sports are another good avenue where your 5-a-aside soccer team might be very homogenous but the league obviously isn't.