Folger Shakespeare Library in Washington, DC, should be at the top of the list of possible research destinations. Along with its extensive and comprehensive collections of rare books, the Folger also provides online access to its Digital Image Collection. It is also worthwhile to browse Folgerpedia, an online resource that promises to offer "all things Folger" for online viewing.
2016 is the year of Shakespeare's death, so the Folger is also sponsoring The Wonder of Will, "celebrating Shakespeare and his extraordinary legacy through special events, exhibitions, performances, and more."
For information about how to become a reader at the Folger and for information about travel and accommodation, please contact Thomas Dabbs at emdhjapan (at) gmail (dot) com.