There's an awful lot of of absolutes being thrown around in here... I'm not willing to crown any of them "best". There are too many I still haven't tried and I've had over 30 brands, possibly many more. My hope is the best is still out there waiting for me to find it. But for the time being, Dog N' Suds it top shelf - if you haven't had it you should, especially if you're a connoisseur.
Locally, I'd have to agree with Weber's. But you need to get it there from the tap - the bottled Weber's uses high fructose corns syrup, but at the tap on Peoria it's made with cane sugar.
The best I've had anywhere is Ithaca Root Beer, a local brew in Ithaca, NY.
If you want a real treat, try Boylan's Original Birch Beer. Can't find it locally anymore since Reasor's doesn't sell it anymore but it was fantastic. The closest thing I can think of that tastes like it is Beeman's gum.
A&W...I still remember when I was a teenager working for a guy one summer setting up double wide mobile homes, we went to A&W for lunch, I got a burger and the root beer. Maybe it was it was so hot, but that was the most satisfying soft drink I can remember.