Looks like a good route with a few adjustments needed. Hayes and Eads both have protected bike lanes.
There’s construction going on at Eads St/Army-Navy Dr making the sidewalk unusable, and the street is not bike-friendly, so I recommend turning off Eads a block early onto 12th St. Also, since you’ll be so close, why not ride through Long Bridge Park? It’s got a cool elevated part near the north end that gives a view of the airport, Pentagon, Air Force Memorial, and DC along with a nice elevated esplanade (map uses the term) that parallels the train tracks (bonus if you have a train sighting). I would avoid riding on the street on Crystal Dr just north of the Airport Access Rd because it involves merging traffic coming from the right. An alternative is to cut through the trees and through the Crystal City Workout Park.
I made a quick route with my adjustments. It’s a little longer than the 2-3 mile length at 3.5 miles, but the view in Long Bridge Park would be worth it. https://www.strava.com/routes/8954453
Bonus history: on Eads St (and Commonwealth Ave in Alexandria) used to run the Washington Alexandria & Mount Vernon Electric Railway. It had a junction (named Arlington Junction) located in the block of buildings surrounded by Eads St, 12th St, Army-Navy Dr that you’ll actually pass by on the route (dunno if there’s a historical marker, but it’s something cool to point out).
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