Our major food bank distributor here doesn't take fresh food any more. But I've had great success with soup kitchens from our local churches taking whatever unwanted meats and fresh (as in nice, not on its last legs) produce.
If you have a Craig's List in your area you can look for "food" under the wanted section, or you can post an ad in whatever section is appropriate (for me it would be free).
We do have a great program for our farmer's market, if you are already on most forms of assistance you can get a $5.00 food voucher to use at the market. There is a limited number of vouchers for those over 65 on no assistance as well.