I figured I'd start off with something simple. It seems that the most popular off-beat monument in the DC area is the Albert Einstein memorial at the National Academy of Sciences. It's so popular it even has a page on Wikipedia. It's also one of the easier to find. The memorial requires just a short walk from the Lincoln Memorial over to Constitution Avenue.

From Pictures of DC

The structure of the memorial is itself somewhat interesting. The base of it forms a map of the cosmos as they appeared in 1979. The downside to this is that you basically have to sit in Einstein's lap in order to see the pattern. I confused a very nice French couple by referring to this out loud as "creepy". I wound up spending a few minutes stumbling over a variety of English synonyms for creepy before finally winding up with "not comfortable". They either understood or were polite enough to feign understanding so I would go away.

From Pictures of DC

The statue gives Einstein something of a "Michelin Man" look. A little bulbous and very out-of-focus. It's a pretty stark contrast to the looks-conscious realism that encompasses so many Washington monuments. This seems to make Einstein even more flawed than he was in real life. It depicts him as tired, old, and somewhat uncomfortable. It's probably similar to how Einstein felt about himself, but I can't verify that.

It's nice, there are signs to it. It certainly won't make the list of my favorite monuments in DC, but it's a good change of pace from the sword wielding, horse-mounted, eyes-upward memorial that you find on every street corner.