This is not a proper answer. Its more a collection of notes gleaned from different sources. Feel free to add more if you find other things.
The first Tour de Trump, a 10-day, 837-mile bicycle race through five Eastern states http://www.nytimes.com/1989/05/15/sports/dispute-mars-end-of-the-tour-de-trump.html
Other site says 825 miles total, or 782 miles. 10 stages in all.
Prologue Albany, MAY 5, 1989. A 2 mile time trial to establish a race leader
Stage 1 - May 6th. First stage was in Albany NY to New Paltz (110 miles), on May 5. This segment is remembered for a hellishly difficult climb called Devil's Kitchen. Officially named Platte Cove Road but dubbed Devil's Kitchen for a nearby mountain hollow, the climb was a 15-degree grade in West Saugerties that ascended from 300 feet to 1,840 feet above sea level in a span of two miles. This part of the route is https://ridewithgps.com/routes/2746243
Stage 2 - May 7th between New York and Allentown on Sunday, May 7. 123-mile route ran due west from NY through New Jersey, over rolling hills and into a head wind, before ending in Allentown, Pa.
Stage 3 May 9th. GETTYSBURG, PENNSYLVANIA, AND WINCHESTER, VIRGINIA
Stage 4 May 10th. BETWEEN FRONT ROYAL AND CHARLOTTESVILLE, VIRGINIA 107-miles
Stage 5 or Stage 6 14.5km ITT in Richmond
Stage 5 or Stage 6 - MISSING
Stage 7 team time trial in Richmond, Va
Stage 8 68-mile circuit race in Arlington, Va
Stage 9 - May 13th Baltimore criterium, a 30-lap, 51 miles
Stage 10 - May 14th The 1989 Tour de Trump ended with an ITT in Atlantic City on a Sunday, just before the Trump Plaza Hotel & Casino. 38.6km The 24-mile time-trial course started in front of the Trump Plaza Hotel and Casino, continued a mile down the boardwalk, took a hard left through a slum area, passed in front of the Trump Castle and took a right over the Brigantine Bridge. From that point the course became a maze of turns through Brigantine Island. From http://forum.cyclingnews.com/viewtopic.php?f=21&t=30224
Three "non-Trumpian" towns through which the race passed: New Paltzes (N.Y.) and Front Royals (Va.) and Allen towns (Pa.) Also, the first six stages of the Tour passed through the Catskills, the Poconos, Pennsylvania Dutch country and the Blue Ridge Mountains and had the feeling of a European road race—rolling hills, open countryside, winding roads. From http://www.si.com/vault/1989/05/22/119927/the-wheels-of-fortune-the-tour-de-trump-billionaire-donald-trumps-bike-race-through-the-american-countryside-was-a-smashing-success
Here's the only "map" I could find, in two pieces.
From "Spy Magazine" and by "SYDNEY SCHUSTER" original link at https://sydneyschuster.wordpress.com/2016/03/03/run-amok-mapping-the-tour-de-trumps-mishaps-foul-ups-and-egregious-exaggerations/
One other reference to a map for this year:
Article "What's in a Name? It's Tour de Trump"
By MALCOLM MORAN, Special to The New York Times
Published: May 5, 1989, map of Tour de Trump route (pg. D23)
1990 Tour De Trump
Suggested plan in 1989 was "Begin the Tour in Boston, steer it down the coast, to Washington...Philadelphia...Detroit...Chicago—go west, young man!—to San Francisco, before concluding the show in L.A. " but this was written in 1989. Probably a grand plan that was changed a lot.
The plan had changed by February
Trump joined Delaware officials in Wilmington to discuss details of the race, in its second year. This year's event will begin in Wilmington May 4 and conclude more than 1,000 miles later in Boston on May 13.
13 stages in this year.
1991 Tour Du Pont
Race was organised/directed by a group/company called "Medalist Sports Inc." of Richmond, Va, according to http://articles.baltimoresun.com/1990-11-16/sports/1990320048_1_tour-du-pont-tour-de-trump-medalist-sports
Eileen Webber, a spokeswoman for Du Pont, said: "We just made the announcement of our sponsorship of the race and, as yet, we haven't had a chance to negotiate with any cities. I'm sure most the cities involved the last two years will be high on the list for the race next May." Same source.
So the first Du Pont one was probably pretty similar to the earlier two courses.
1996 Final Year.
Won by Lance Armstrong, 12 day event.
A random image found