A lot of cities have these wonderful little things sprouting up called "community gardens" and depending on what yours offers you might be able to turn a family activity into some extra food for your table.
Where we live, the local Parks & Recreation Department has a section in one of the parks fenced off for these awesome 4'x8' raised planting beds. If you are a resident of the area you can "rent" one for 6 months at the cost of $12.50 or you can get it for a full year for $25.00. Considering the cost of fresh fruits and vegetables, this is real deal!
My kids and I have rented one for a full year and this will be our first year trying to be "urban farmers" but we are excited about the prospect of growing our own produce!
So look into your local parks and see if they offer anything similar. Not only would a garden like this give your family a sense of accomplishment, but it can teach your children about responsibility and get them more involved in making healthy eating choices.