Welcome to the neighborhood. I’m on Harvard St just on the Columbia Heights side of 16th. This is a great neighborhood for biking – everything is super close – until you try to come home and you have to go up a giant hill.
I’m not sure what the best way for you get up to Tenleytown is. If I were you, I’d try heading up 14th, which has a nice bike lane, and turning left on Upshur. Right on Mathewson, left on Blagden, right on Beach, and left on Broad Branch. From there it depends on exactly where you’re going.
I don’t know any of these roads past Upshur, but I know that Beach is closed on the weekends to car traffic, and it’s like a bike wonderland. So I can only assume that the roads surrounding it are bike-friendly.
As everyone on here will tell you, try it on a weekend if you can to get an idea what it’ll be like. And if you have questions about the neighborhood, let me know. My wife and I have been here for 5+ years, and we love it (both before and after having kids)