Can the DC dopers tell me which Metrorail stop is highly prefered by little legs too big for a stroller? As I recall, the Adams Morgan stop (after a long escalator)leaves you at virtually the bottom of quite a climb to the Zoo. What about the Cleveland Park stop? Is it flatter but further from the Wash Zoo?
I’m sure the FONZ would know! 
What about the Woodley Park-Zoo stop? Unless they renamed it that’s the one not far from the zoo entrance.
Yeah, the Woodley Park Zoo stop is one and the same as the Adams Morgan stop. 
Go to the Zoo via Cleveland Park . It’s one more stop on the red Line going north, but it puts you uphill of the National Zoo. Then you and yours walk downhill to the Zoo, and Bob’s your monkey’s uncle. As I recall the Cleveland Park metro station has exits on both sides of Connecticut Avenue - you want the East side exit so you don’t have to cross Connecticut Ave.
When you leave the Zoo go downhill to the Woodley Park-Zoo-Adams Morgan station. Again, you’re going downhill. 
I think the Woodley Park station is closer to the Zoo entrance, but the uphill trek is a bit much for younguns. And olduns. You do have to cross Coneecticut Ave to get to the station, but it’s not too bad.
There’s a lot of walking at the National Zoo. Worth it, but wear very comfy shoes!
Are you new to the DC metro? If so, consider getting your fare cards in advance. Learn more about the Metro before you go, especially with kids in tow.
Oh, and enjoy the Zoo - it’s great!
Typo Knig, it’s been awhile since we’ve been able to get back to the DC area. I recall the Metrorail used to offer like a flat-fare for a card good all day long. It may have even been offered on weekends, but I cannot recall. I WAG those days are long gone, huh?
I’ve been to the National Zoo once. Got off the subway and saw a big crowd lined up at the bottom of the escalator. No problem, I thought, I’ll just take the stairs.
I believe that Cleveland Park is actually marginally shorter a distance. Very marginally mind you, like a few feet. But like has been said, it’s uphill from the Zoo so it’s an easier walk.
And yes, Metro still has one-day passes for $9.00.
As Typo Knig says, you can disembark at Cleveland Park and then go to the Woodley Park-Zoo stop when you leave, so you’ll walk downhill both ways.
Important note since it doesn’t sound like you’ve ridden Metro recently–if you are parking in their lots, you must buy a SmarTrip card as no cash/credit cards are accepted. The funds on the SmarTrip card can be used for both the parking fee and the fare.
You’ll want to consider whether the 1-day pass makes the most sense. It’s the best option if you’re doing a lot of getting on & off, but if you’re just going to the Zoo and back it’s probably cheaper to buy regular fare.