Where did "humongous" first appear?
J.E. Lighter, Random House Historical Dictionary of American Slang (1997) has this entry for humongous:
humongous adj. {sugg[ested] by huge and monstrous, with stress pattern of tremendous} Stu[dent] Also humungous, humongoid, humongo. [Earliest three cited occurrences:] 1968 Baker, Ladd & Robb CUSS 141: Humongous {amount}. A great deal. 1969 Current Slang I & II 53: Humangous, adj. A unit of measure one size larger than monjorious.—Air Force Academy cadets. 1972 N.Y.U. student: Humongus means like gigunda, only bigger.
The earliest match I've been able to find for the word (in the variant spelling humungus) is from a fraternity party advertisement in the [University Park, Pennsylvania] Daily Collegian (February 25, 1966):
Delta Chi, Alpha Sigma Alpha and Phi Kappa Tau Present a Big Humungus Triad at Delta Chi
However, supersleuth EL&U participant JEL has uncovered an even earlier instance of the variant humongus in Janice Higginbotham, "Students Display Varied Expressions and Sentiments," in the [Milledgeville, Georgia] Colonnade (March 17, 1964):
Sentiments, or "words of wisdom" can often be heard because of trying things. Typical of this is when someone enters the "Big S.U. [Student Union]" and comes out with the "classic statement," "just ask me if I didn't fail that "humongus" test."
The Colonnade was the student newspaper of Woman's College of Georgia, now known as Georgia College and State University. In 1965 it had an enrollment of 1,002 students. Two months later, as EL&U participant shoover points out in a comment beneath this answer, a parody issue of the same student newspaper includes an instance of humongous. From Gwinn Leverett, "Please, De-Bees," in the [Milledgeville, Georgia] Columnude (May 29, 1964):
One student reported that she grabbed a bunch of leaves, as she always does when passing a bush, but to her shocked reflexes she discovered that she had grabbed a handful of Bee. The sting had such a traumatic effect on this particular student that she is now afraid to grab any leaves. Other students make wide detours to avoid the humiliation and fear of being chased and attacked by the humongous number of bees in front of Atkinson.
Evidently, humongus/humongous (very likely pronounced with a short o rather than a short u in the second syllable) was in reasonably widespread use at this college in Georgia by the end of the 1963–1964 school year.
An instance of humungous appears in another student newspaper—this time the one at Hardin-Simmons University in northern Texas—in late 1967. From Gary Stratton, "Coogs Take Eagles to Flush Season," in the H-SU Brand (November 21, 1967):
A "humungous" crowd of 16,000 people witnessed history here last Friday night at P. E. Shotwell stadium. Those fans saw the amazin' Cooper Cougars trounce the cross-town rivals, Abilene High, for the District 2-AAAA undisputed championship.
We thus have five instances from 1964 to 1967—from a small college in Georgia, a large university in Pennsylvania, a small college in Iowa (cited in user121863's answer), and a smallish regional university in Texas. Geographically, that represents a considerable range of occurrence—and underscores the origin of the word in student use.
Humungus also appears in Glen Gainsbrugh & Peter Whitehead, Two Travel Through, Or, The Skinny Shall Inherit the Earth (1968) [combined snippets], where the narrator is evidently a student, but the publisher is a major imprint of the time, Signet Books:
Things went all right at Annie's for about a month. There was always something around to eat, and David and I joined the Boston public library and studied most of the day. I could feel my brain groaning with all the knowledge being put inside, and every once in a while it would revolt and give me a humungus headache, as though it was trying to tell me that it was happier fooling with a carburetor than figuring out Kant's Preface to Future Metaphysic.
Green’s Dictionary of Slang has the earliest usage example from 1967;
humongous adj.
also humangous, humongeous, humongoid, humungous, humungus [sugg. by SE huge/monstrous/tremendous] (orig. US) enormous, outsized, huge.

1967 - Cosmos (Coe College, Iowa) 5 May 2/4: Maybe at the bottom there will be something worthwhile that us humble sheep, your poor blind, flock, will gather around that humongous soapbox in the sky to listen to.
but, as it often happens with slang terms, their usage predates evidence in writing. The following source suggests that the term was actually used in speech from early 1950s:
From Verbatim: (1978)
Among words that are likely to be included in dictionaries before long is humongous.....It has been in consistent popular use since the early 50s.
One of the entries above has the origin partially correct: "1969 Current Slang I & II 53: Humangous, adj. A unit of measure one size larger than monjorious.—Air Force Academy cadets." I once had a dictionary that gave the origin of humungous as being from some cadets at the Air Force Academy in 1959. The definition they had for this word that they created was "A unit of measurement one unit larger than mungous". So, I looked up "mungous" and it was the same Air Force Academy origin, and the definition of mungous was "A unit of measurement one unit less than humungous". Having been an Air Force Academy cadet myself, I can attest to this being the type of humor that was a part of the culture of the time at the Academy. Humungous became a popular word, but mungous did not stick. Still I prefer the cadet humor embodied in the original definition.