There are a few on-base hotels that family members of graduates can reserve.
Please note - they have very limited availability and you can get “bumped” if there is a more pressing need from active duty members. There are many restrictions that further make it hard to stay on an on-base hotel. Because of this, we highly recommend you book a hotel in the area - as it will guarantee your reservation, generally provide better amenities, and allow you to book sooner than the on-base locations generally allow.
Below are links to the on-base hotels by branch and base:
Great Lakes: https://www.navy-lodge.com/lodge_page.html?p_lodge_number=5
Ft. Jackson: http://discoversouthcarolina.com/products/716
Lackland AFB: http://afwm.org/travel/base-lodging/
MCRD San Diego: http://www.mccsmcrd.com/lodging/
MCRD Parris Island: http://www.recruitparents.com/bootcamp/billeting-pi.asp
Camp May: no on-base housing for family members of graduates.