My current favorite burger place is The Counter
--there are quite a few of them in the LA area but none in Vegas yet (which makes it a rare treat for me).
If you can make it to Reston, they do indeed offer avocado
on their burgers. It's pricey--in the neighborhood of $10-12 bucks for a burger once you get through with it--but it's worth it every now and then. The fried pickle chips and sweet potato fries are great, too. But it's definitely not an everyday thing.
I'm just bummed that they're opening them in Dubai and Saudi Arabia, but not Las Vegas yet. Then again, there are already tons of upscale burger joints on the Strip, so I've got no shortage of places to score pickle fries.