1. Nape of the neck. There’s only one nape, and it’s the back of your neck. It’s possible we get confused by the “scruffs” of animals’ necks since there are other scruffs out there. If you’re ever talking about a nape, though, you can drop “of the neck.”
2. False pretense. This is one we all should have known before. Although pretense technically means any “claim or implication,” the vast majority of the time, our usage of “pretense” already implies falsehood. For example: when’s the last time you thought something was both pretentious and genuine?
3. Frozen tundra. “Tundra” comes from the Russian word for Arctic steppes, and tundra is generally characterized by permafrost, frozen subsoil. Technically, there is non-frozen Alpine tundra, so-called from lack of vegetation, not temperature. Still, the vast majority of tundra is frozen. So, whether you’re talking about northern Siberia or poking fun at North Dakotan winters, this phrase is generally redundant.
One common in my area is "Where are you located at?" which could be two words shorter. Mental_floss has more, with dozens more in the comments. Link
(That's an example of a pleonasm, not a comment on Neatoramanauts :) )