I have used the vinegar solution in the past with mixed results. It seems to work well on broad leaf weeds, but struggles to kill the hardier stuff.
In areas were I don't want to use herbicides, my handy dandy flame thrower purchased last fall from Harbor Freight works great. It has several advantages herbicides do not have.
1. It is unaffected by weather. While I've never done it, I suppose you could use it while it was raining and still kill the weeds. Most herbicides have a four hour window before rainfall for them to work. In fact, what I've discovered is that it's great to use after a rain shower as it seems to work even better when the weeds are wet.
2. It screws into any 20 pound propane bottle. So you can "rob" the bottle off your BBQ grill for a quick job and be grilling steaks when you're through, (I've been tempted to cook a few steaks with my flame thrower, but haven't taken the plunge as of this writing).
3. You get to play with fire. 'nuff said about that other than keep a water source handy if you're fearful of it getting out of control.
4. It's a multi-purpose tool. When I rebuilt my old disc harrow this past spring, the bolts holding the bearings in place where rusted solid and to the point of being so eaten up with rust and "blisters" that no wrench could grab them well without the danger of rounding them off. I hooked up my ever so happy to help flame thrower and blasted each bolt till red hot and then doused each one with used motor oil. Fire, smoke, boiling oil . . . . each bolt came out with ease.
Additionally, before I set out my tomato patch this spring, I "flamed" the ground with my "breath of the dragon" flame thrower to kill any blight or powdery mildew that might be living in the soil. Worked like a charm. AND . . . it works great to start a bonfire which of course, impresses the pants right off any observers who might have stopped by to share a cold one and some conversation.