WGBH Discounted Rates ("just notify the hotel (you) are WGBH ... guests and would like that rate if available."):

Double Tree
$219.00 per night. Please note they are remodeling the property, which is a Hilton and owned by Harvard University. 1 mile from the BPL.
The Lenox
$245/night - it is located near Copley Square (right next to the BPL itself).

BPL Discounted Rates:

Charlesmark Hotel (0.1 miles from the BPL, limited number of rooms as a small property). To access the rate, call them and use the keyword "BPL Partner 2013" (stress "call" - this code is not recognised on their website: they're very helpful.)

Standard Rooms: $189 per night plus 14.45% tax per night. Appx. 200 square feet, 12’x12’ plus bathroom with shower. One double bed, large leather reading chair, small desk writing surface. Residential view only.
NOTE: Only two rooms available June 3 - June 6. There are more rooms available if doing June 4 - June 6.

Queen Rooms: $219 per night plus 14.45% tax per night. Appx. 250 square feet, 14’x18’ plus bathroom with shower. One queen bed, small sofa with twin pullout bed, desk writing surface. Views of Copley Square or residential views.
I'll likely try to find a cheaper hotel that can easily access the BPL via public transit next week. No guarantees on the success of this.

There is also the option of staying in Cambridge and walking over the bridge into Boston. Or staying in Harvard Square or Kendall Square (near MIT) and taking the 'T" (MBTA) to the BPL - redline to greenline changing at Park St.

The nearest airport is the Boston airport (code: BOS). The BPL area is a ~35 minute public transit ride from the airport. To get from the airport to the BPL, take the free airport shuttle to the Blue Line station. Take an inbound train towards Bodoin Station. Once you reach the Government Station stop, get off and take any outbound Green Line train to the Copley Square stop (where the BPL is located).

The airport does also have shared Shuttle Service (~$20 - $25) and taxis (unsure of the cost).