Crime here is indeed minimal and I've never heard of anyone being assuaulted in the street in the five years I've been here. The corniche is a nice place for a walk at any time and there are some nice leafy back streets here and there. However, Doha Traffic's very bad and few roads have pedestrian crossings, so strolling out in the evening (shops and banks are open then, by the way) can be dangerous and unpleasant. You wouldn't want to think of your kids out there.
Solitary females can get stared at and made to feel uncomfortable (some western women cover up with an abaya if going out though it seems to be Asian-looking ladies who are subject to the worst harrassment) but actual physical assault is virtually unheard of.
As regards meeting the locals, you won't much. There are very few Qataris in the front line of retail or commercial hospitality and although Arabs take great pride in courtesy and hospitality, Qatari society is very family centered and religious, so in practice you'll probably only get to know any Qatari colleagues you might have. There is a small bar culture, mind you, and a few Qatari men venture into that.
Most Westerners and Qataris spend more time in malls than on a street.