What is the name of the ambiguity in the phrase "I want to visit clubs with attractive women"?

Solution 1:

Your sentence contains an example of ambiguity resulting from a misrelated construction. The Oxford Dictionary of English Grammar defines misrelated as follows:

Not attached grammatically to the word or phrase intended by the meaning, either joined to the wrong word or phrase, or completely unattached.

Although terms such as misrelated, dangling, hanging, unattached, etc. are most commonly applied to participles, verbless phrases can also be misrelated.

The offending misrelation in your sentence is not a participle but a prepositional phrase.

Solution 2:

I think this is called Amphiboly. The first example I ever read was the phrase "half baked chicken".