As a WDW vet, HydroGuy's guide to DLR for WDW Vets is a good place to start.
http://www.disboards.com/showthread.php?t=1162599
If you only have one day, you will probably have to made some choices about things to do and things to leave out. You asked about both DL and DCA, so I'm going to guess you'll get a park hopper ticket. The two parks are about 100 yards apart, so it's pretty easy to go between them. Think of it like going from Future World to World Showcase.
Over in DCA, I would make a point of checking out Carsland and riding RSR. If you like thrill rides, CA Screamin' is a good choice. I'd probably skip Soarin' and TSMM (pretty much the same as at WDW). ToT is similar, but not identical. If you're there when it's running, Mad T Party is fun. The Aladdin stage show is pretty impressive, but it's a huge time commitement (the show is 45-minutes).
For me, there would be more "must do" level rides over at DL. If you just wanted to focus on the unique, I would ride Matterhorn, some of the Fantasyland rides (e.g., Storybook Canal), and Indy Jones. Other rides that are similar, but different, are PotC, Big Thunder, IaSW, Space, Splash, HM, and Buzz. When are you going? If it's during Halloween and/or Christmas, then some of the rides might have an overlay. From mid-Sep to Halloween, Space has the Ghost Galaxy overlay. From mid-September through New Year, Haunted Mansion has the Nightmare Before Christmas overlay, and from mid-November through New Year (at least), Small World has the Holiday overlay. I would definitely ride any of the rides with the overlay.
In terms of the nighttime shows, they all require a time commitment if you want a good spot. With only one day, I would probably forgo them on this trip.
Also my hotel is nearby, The Menage...anyone familiar? Is it walking distance?
It depends a little on how much you like to walk. From what I can tell, the Menage is at the corner of Harbor and Ball. I think you have two options to walk to DL. If you walk south on Harbor, you'll come to the pedestrian entrance to
Disneyland. It's about 0.8 miles. You could also walk to the Mickey & Friends parking lot and take the tram to DLR. I don't know how far that is.