Leave the Stroller in the Hotel
While Washington DC is a walking city that's easily accessible with a stroller, all buggies (including fold-up umbrella strollers) are prohibited from entering the Washington Monument — and there's no place to store them while you're there. So you'll want to leave the stroller in the hotel or with someone who's not planning on going inside the monument while you're there.
While you're at it, park rules also prohibit food, drink (except bottled water or baby formula in clear plastic containers), and large backpacks from entering the monument, so you'll want to leave those things behind as well.
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