Well… I made this answer easy for you.
Me (and a team of geeks) took a look at the data that is available to the public by the NOAA National Climatic Data Center and extracted the most important bits pertaining to when you can start growing basil. I made a nice little table for each state and area showing you exactly when you can start planting your herb gardens, based on 30 years of data. We had to do some serious number crunching here to provide you with this easy-to-digest information, but we did it. Just for you.
Below you can find a link with information for each state. Each state’s page will give you the following information:
Note: Keep in mind that basil likes to be warm, so you may want to adjust your start date accordingly.