I'll do Braniff's nonstops from DFW, from their April 25, 1982 schedule, along with the number of daily flights):
Amarillo (4x), Austin (8x), Chicago-O'Hare (7x), Corpus Christi (3x), Denver (8x), Harlingen/Brownsville (3x), Honolulu (1x), Houston-IAH (16x), Kansas City (10x), Las Vegas (4x), London UK (1x), Los Angeles (5x), Lubbock (5x), Memphis (3x), Mexico City (2x), Miami (5x), Midland-Odessa (3x), Minneapolis-St Paul (3x), Nashville (1x), New Orleans (6x), NYC-LaGuardia (5x), Newark (3x), Oklahoma City (9x), Omaha (2x), Orlando (1x), Philadelphia (3x), Reno (1x), San Antonio (11x), San Francisco (3x), Sea-Tac (3x), Tampa-St Pete (2x), Tulsa (7x), Washington Dulles (2x), Wichita (4x)
34 cities, 154 flights. I don't have an AA schedule from that era, but, hopefully this'll help, and someone else will be able to help you with AA's info.
Tom in NO (at MSY)
"The criminal ineptitude makes you furious"-Bruce Springsteen, after seeing firsthand the damage from Hurricane Katrina