Apartments can be a great place to grow orchids or other interesting plants. But if you do not have much sun, you will only be able to grow houseplants that can take low light. As for vegetables, the only alternative I can suggest is a community garden. Fairfax and Arlington counties have several community gardens. They are all popular and have waiting lists, but people do move about in this area so it is worth signing up if vegetable gardening is a passion for you. Contact the Cooperative Extension office for your county. They are online at ext.vt.edu, there you can find the closest community garden to you and other gardening opportunities such as volunteering to help maintain a garden at Green Springs.
If you have the time and money try one of those indoor lighted herb gardens. If you love fresh herbs this would be a great way to have fresh herbs at your finger tips.