The traditional story is that Predator is predominantly set in Val Verde (for anyone unaware, this is a fictional Central American banana republic that appears in a few 80s/90s action movies, originally invented for Arnold Schwarzenegger's Commando so as not to offend any real Central American banana republics).
However, Val Verde is never mentioned in the film, nor is it mentioned in the novelisation. So where does the film take place?
The novelisation states that the opening briefing with General Phillips takes place in Conta Mana, which (so far as I can tell) is a similarly fictional Central American nation, said to be on the Pacific coast. But this isn't where most of the action happens, of course — Dutch and co. head "over the border" by helicopter before dropping into the jungle. The book is never outright explicit on which nation is across this border, but it's strongly implied to be Guatemala. This would seemingly tie in with Predators almost 25 years later, in which Isabelle claims the events of the first film took place in Guatemala.
But it's not quite that cut and dry. The comic Predator: Concrete Jungle has a section where Detective Schaefer retraces his brother's steps in Central America, hoping to find out what happened to him, in the process travelling to several locations from the film — including the ruined guerrilla camp and the crater left behind when the Jungle Hunter blew himself up. I've not actually read this comic, but the novelisation of it states that Schaefer starts his journey in Panama before heading north. While Guatemala is north of Panama, it's almost 600 miles away, with no less than four other countries in between — Costa Rica, Nicaragua, Honduras and El Salvador. The novel makes it sound like Schaefer merely hitches a ride with somebody, so it seems highly unlikely he went all the way to Guatemala.
His journey eventually takes him to a small town — little more than a few huts in the jungle — called Riosucio (a quick Google reveals there are a couple of towns called Riosucio in Colombia, but I'm willing to believe this one is just an invented location for the book). Here we get an interesting line that describes Riosucio as being "at the foot of the ridge that marked the border between this particular stretch of malarial rain forest claiming to be a nation, and the next, equally backward chunk of jungle". It goes on to state that Dutch and his men crossed this ridge into the adjoining nation on their mission, back when "this particular pair of banana republics had been closest to escalating their perpetual disagreements and border incidents into something bloodier and more formal". It's far from definitive, but to me those descriptions would not seem to imply any of the aforementioned, real-life Central American nations, but two smaller, fictional states. Follow this logic, and Riosucio could well be in Conta Mana, while the neighbouring "equally backward chunk of jungle" could be Val Verde. As an aside, the novelisation of Predator does indeed mention the insertion helicopters crossing a ridge on their way over the border.
None of this seems all that definitive. I've often tried searched for some more concrete evidence regarding where Predator is set, but the only source I've ever found linking the film with Val Verde is an interview with Stephen E. de Souza — he wrote Commando and thus basically invented Val Verde, but he had no involvement with Predator. Not to mention the quote in question is framed in the context of him "believing" the film is set there, as opposed to knowing for certain. I believe NECA have also mentioned Val Verde on the packaging for some of their Predator figures, but I suspect that might be a bit like the name of the planet Calpamos in Alien — a case where something has been assumed and later accepted by the fan base, becoming so well-known that it's later crossed over into semi-official media.
Thus, the only actual on-screen, definitive clue we get to the film's location is Isabelle's mention on Guatemala in Predators.