Question
We live in California near the sea, an hour from Oregon. We don't want to use a product like Weed & Feed but want to greatly reduce the weeds in our lawn. We hope to do some organic vegetable gardening. Our niece lives near the Finger Lakes in New York and says they have no weeds to speak of in their lawn and don't use anything and that everyone else's lawn around there is the same. How can that be possible and how can we kill weeds in our lawn without killing the lawn or harming our cats?

Answer
There are four options for maintaining a weed free lawn:- cultural, manual, mechanical and chemical. You want to rule out the last one. Therefore you will have to exploit the others. It is not possible for me to go into details because there are many things that I do not know about the general conditions out there and even less about your specific conditions. The following are for your consideration. Approach each with the primary purpose of weed control and you will achieve success.
Cultural: The things you routinely do to grow a good lawn and has to do with mowing height and frequency, watering, fertilizing etc.
Manual: Hand work like pulling weeds, raking debris, hoeing areas adjoining the lawn from where weeds can spread out. You can include things like resodding bad patches and installing plastic edging etc.
Mechanical: Involving machines and can be considered as cultural also. Periodic operations like aerating and verticutting achieve some weed control as a side benefit.
You will undoubtedly hear of things like vinegar, sugar and molasses, baking soda etc. as alternatives to 'chemical' applications. I'd like to point out that 'there are no safe chemicals; only safe ways of using chemicals' and 'the danger is in the dose'. You have to assess these two statements when considering the application of any product on your own environment.