Creating a view from multiple content types where one is optional
Install the Entity Reference module, and create an entity reference field on your Content Type B. Configure the field to reference Target Type Content and Target bundle Type A. Lets call the field ref_to_a.

Set up a view of Content Type A as a table of fields. Add the Title and Body fields. Then under Advanced add a Relationship. Use Entity Reference: Referencing Entity and choose Content referencing Content from field_ref_to_a Do not set the relationship as required, as you do not want to exclude the Type A records which do not have a Type B referencing them.

Now add a Content:Body field to your view, and configure it to use the relationship you have just created.

This should give you a view which will look like:

New York    Something
Ohio        Something   Interesting tidbit
Virginia    Something


Adjust your formatting as required, and good luck.