For at least the first part, I recommend 3rd (I dunno where you’re starting, so watch crossing Blair Road) to Kansas to 13th to Spring to 11th to Vermont to R to 15th to Rhode Island to M to 21st to H. I know the bit from 3rd to 11th really well and it’s pretty mellow. I don’t know the second part from regular use, but it seems sensible. This isn’t quite the route Google Maps/Bicycle recommends, but it’s a start.
I used to ride much of this route. The recommendation of 3rd to Kansas is spot on. I’m not sure I ever really found a good solution to the latter part, though I only had that route for a few months. I will say I’d probably prefer 14th to 13th, as soon as feasible, and maybe try that to Rhode Island (which I was not especially fond of). There probably are fine routes for the lower half, I just never found them (and it was nearly 20 years ago).
An alternative is Piney Branch to Rittenhouse, then to Joyce and down to Beach Drive and the RCP Trail. You can take that all the way to Pennsylvania. That’s actually a pretty mellow commute.
The Zoo closes the part of the trail near it at night. If you are interested in this route, let me know and I’ll post my ways around. To be honest, that stretch of the RCP isn’t my favorite anyway. Basically, l rode on the eastern side through Adams Morgan. Most of that route is either pretty calm and/or has bike lanes, till you drop down in to Park a bit farther North.
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