Walking distance is of course an individual range, but if you're bold enough to handle the Folklife Festival in July, then unless you're actually wrangling muppets at the same time, I believe you could handle each of the following properties (although I would recommend an early morning takeoff for comfort):
JW Marriott (usually superb service - but also usually the costliest)
Marriott at Metro Center - my overall favorite for location and service, but of course to each their own
Residence Inn - DC Capitol - actually one of the closest, but south of the mall, so further to other areas (if relevant)
Courtyard Convention Center (not a CY fan - so I'll let others speak - but it is within walking distance)
As a DC native, I often do weekend tours for family and friends and we've made leisurely walks to the Mall from the Mayflower, Downtown Renaissance, and even the Fairfield (north of Verizon center), but I emphasized 'leisurely'. If you're jousting with the folklife crowds each day, that 'stroll' may be extra energy you'd prefer to invest on the mall going elbow to elbow with the visitors.
I suggest looking at the Marriott.com map of these properties, throw a few addresses along with one of the Smithsonians onto Mapquest, (the festival runs from the west around 14th St.-Smithsonian History/Technology to the east 7th St. - toward The Capitol) click the walking icon to get the distance, factor in the hotel rates (still, at this point, surprisingly decent AAA rates for say, the July 5-8 weekend) and reserve soon, one or two locations (that can be cancelled) to lock in the decent rate (if they go down, revise the reservation) and keep gathering info. And as always, hydrate early and often. Have fun, it's an excellent event.
I'll second the Marriott at Metro Center. Stayed their a few times and it is pretty much in the midst of all of DC. The metro is an easy walk and short ride to DCA and some great dining in the area.
Hey erc, What is the name of the restaurant in the same block as the hotel where but it seems every political aid lives in that joint, very fun to people watch and the food is pretty good as well?
Oh man iahflyr, I knew that stuff (The Monocle or Hawk and Dove etc) back when as Billy Joel would say, "I wore a younger man's clothing", now I'm more likely to know where the AARP lobbyists hang out. Two nearby restaurants that are pretty trendy (and tasty) and therefore might lead to good people watching or political aides dining at the taxpayer's expense, are, Zatinya, a tapas type place created by Jose Andres (Jaleo as well) with a bit of a Turkish flair (Gem Princess is our Mediterranean expert) and Oya with the latest Asian Fusion style.
Old Ebbitt Grill (a Clyde's operation, along with the preferred by me Hamilton, both within a couple of blocks) is a relatively famous hangout as well and the Occidental Grill in the Willard, a bit of a power lunch scene. Oh well, it's brewpubs for me, where the most famous I may meet might be Bob Uecker, "just a bit outside".