Does "That" have to be next to the noun it modifies? [duplicate]

This "that" does not modify a noun, but rather it introduces a restrictive relative clause, and the relative clause is what modifies the noun it goes with. Your examples also involve extraposition of relative clauses, which makes their structure hard to understand.

John held parties for his kids that featured clowns, numerous exotic animals, and lots of food.

This is from the (stylistically inferior and ambiguous):

John held parties that featured clowns, numerous exotic animals, and lots of food for his kids.

Here, the relative clause follows immediately the noun, "parties", which it modifies. So this makes clear the point of extraposing the relative clause to the end of the higher clause.