Lake Whitney is an easy permit to acquire. Whitney is a U.S. Army Corps of Engineers lake and as with all Corps of Engineer property, you have to have Hunter Ed in order to hunt. Here's a link to the Lake
Whitney webpage.
http://www.swf-wc.usace.army.mil/whitney/pages/
Lake Aquilla is a Corps lake but the wildlife is managed by Texas Parks and Wildlife Department (TPWD). You need to purchase a $48 Annual Public Hunting Permit (APHP) from any place that hunting/fishing licenses are sold in order to hunt APHP areas. There is a lot of land in the APHP system. Bowhunters have opportunities to hunt management areas that aren't open to gun hunters. Here is a link to public hunting on TPWD webpage.
http://www.tpwd.state.tx.us/hunt/public_hunting/
Caddo National Grasslands is part of the U.S. Forest Service. Portions of the grasslands are managed by TPWD under the APHP program and part of the grasslands are under Forest Service control. I haven't hunted the grasslands in so long I can't help you with any information.
Ray Roberts and Tawakoni are under the TPWD Annual Public Hunting program.
Lake Benbrook is open to bowhunters and you can still apply for a permit. The next application deadline is in October so you have plenty of time. Benbrook is just outside Ft. Worth. Give them a call and they will mail you an application.
Benbrook Project Office
P.O. Box 26619
Fort Worth, Texas 76126-0619
Phone: (817) 292-2400
Fax: (817) 346-0021
Hope this helps. There are a lot more public hunting opportunites than most people realize. Check with the Corps of Engineers, U.S. Forest Service, U.S. Fish and Wildlife Service (Hagerman NWR and Aransas NWR), Texas Parks and Wildlife Department, U.S. Army (Ft. Hood), some of the Texas river authorities have bowhunting opportunities (Coleto Creek), etc.
So far this season I will be hunting Corps of Engineers (I have permits for Lake Georgetown and Whitney), U.S. Fish and Wildlife Service (Hagerman NWR, Segment D), Texas Parks and Wildlife (Special Permit at Richland Creek WMA) and others I won't reveal over the internet due to the competitive nature of getting drawn for the hunts. Good luck.