Vibes

Vibes is a 1988 quirky romantic comedy. It's about Nick Deezy (Jeff Goldblum), a psychometrist working in a museum, and Sylvia Pickel (Cyndi Lauper), a medium with a Deadpan Snarker spirit guide named Louise. The two meet at a study for psychics, and take a nearly instant dislike to each other.

The two are hired by Harry Buscafusco (Peter Falk) to travel with him to Ecuador to find his missing son. However, Nick quickly deduces that something isn't right, and Harry confesses that what he's actually after is the lost City of Gold.

Tropes used in Vibes include:

Astral Projection: Sylvia can do this with Louise's help. It's hard for her to come back, though.
Belligerent Sexual Tension: Nick and Sylvia are an almost textbook case. Naturally, they hook up at the end.
City of Gold: What everyone is searching for. It turns out that the "gold" is actually a psychic weapon, not a metal.
Defensive Failure: Subverted at the end. Nick has Dr. Steele held at bay with an M-16.

Dr. Steele: Have you even held a machine gun before?
Nick: Sure, lots of times. I was captain of the Automatic Weapons Team in high school.
Dr. Steele (starts inching forward): Don't lie to me. You wouldn't know how to use that thing if you tried.
(Nick points the gun up and fires a few bursts into the air. Steele instantly jumps backwards to where he started.)
Nick: Oh, I dunno. Seems pretty simple to me.

Fantastic Nuke: The Lost City's psychic weapon.
I See Dead People: Well, a dead person, anyway. Sylvia's guide Louise is a ghost. Through Louise, she can contact the spirits of other dead people.
Mayincatec: The Lost City is very much "Hollywood South American Native."
Psychic Powers: Naturally. Not only are the main characters psychics of two different flavors, but the people of the Lost City used them as a Fantastic Nuke.