J.B.
Hi L.! I live in south Arlington, and my oldest will be attending Kindergarten this fall. Like you, we have a really good public elementary school, but our son is very bright and we wanted him to be challenged academically.
There is a charter school near us called Arlington Classics Academy. I've always heard really good things about it. It's supposed to be very academically challenging - the school days are a little bit longer, they teach math a year ahead, etc.
The only thing we don't like about it is how strict they are. They're pretty serious about having a very well-behaved student body. I've spoken to many moms who like the school very much, but they do describe it as being like a military school. That doesn't fit very well with our parenting style, so we're not sure what we're going to do yet! We applied for this fall - they have a lottery, so it's just the luck of the draw whether you get in or not. Maybe you can check out ACA and it will be a good fit for you.
I've also heard about a group of charter schools called Harmony - I believe they have several locations around the metroplex, though none are in Arlington.
As far as private schools go, I've heard good things about Oakridge and Children's University, both on Arlington.
Best of luck to you! This is proving to be a very tough decision for us!!