For the best of the best public high schools in Montgomery County, you want to stick with the 'W''s district of Bethesda/Potomac
Winston Churchill
Walt Whitman
Thomas S. Wootton
and to a lesser extent Walter Johnson. B-CC (Bethesda-Chevy Chase) isn't a bad alternative.
You're right in the backyard of notable private schools Georgetown Prep, Bullis and Landon, among others, and the income based demographics of the cluster and surrounding feeder school areas are an effective barrier to entry to most of the kind of troublemakers you'd probably rather your kids not be around. Massive pressure on those schools to offer the closest thing to a private school academic and athletic environment based on the fact that a massive percentage of households in those areas can easily afford to send their kids to these outrageously expensive private schools, but there is only so much availability to go around, so if a parent is consigned to sending their kid to a local public school, it better be on par with the private alternatives.
A dirty little secret that I have first-hand experience with - although the County would like to present a facade that all students have equal opportunity to access the same educational resourcs at all schools county-wide, that only goes as far as what the PTA contributes to the schools outside of their assigned county-funded budgets. From 2008-2012, my stepson attended an elementary school that fed into Whitman (it had a school-within-a-school...a learning center for kids who had issues or learning disabilities that was far and away considered the best in the county, if not the state), and I immediatly got involved with the PTA. At the first meeting, the library was full of parents who seemed to be just quietly and patiently be waiting for the meeting to end. Over the summer, the school had excitedly announced that they had acquired one Promethian Board for each grade. During the meeting, several parents inquired what it would take for every...single...classroom to have a Promethian Board (those things were new, and cost a fortune). Well, money from outside sources (the PTA), was the wink/nudge/nod answer to that question. By the time the meeting had ended, someone had placed a box by the exit. The checkbooks came out en masse, and into the box the checks went. By the start of the next school year, that school had Promethian Boards a-plenty. More than any other elementary school in the county. The parents saw to that. When he and his Mom moved in with me (still in Montgomery County, but not quite as affluent an area), to put him under one roof and in a two-parent home in 2011, I continued to drive him to that elementary school for one more year, until he'd become proficient enough to not need the learning center environment any longer. I was involved with the PTA in primary, middle and now high school, and my involvement has made it clear that only a handful of parents besides us are putting any private money into the coffers of those schools, and while they're still good schools, from a resources standpoint, they are well behind the 'W''s.
Now, the good news is, if you're willing to do go through the trouble of an arduous process, you don't necessarily have to live in the districts to attend those schools, however you have to make a very strong case as to why, and you have to provide your child with transportation. Not easy, but do-able for a sufficiently motivated parent(s).
Good Luck!