The closest launch to the public for an orbital launch is almost certainly the one you listed, Baikonur. I'm quite confident that for people outside, that is probably about the closest you can get as well. Quite frankly, a mile away isn't very safe to watch a launch...
As for just how close can you get in a protected environment, outside of the spacecraft? There are a few items which I can't determine which would let you be the closest. Contenders are:
- I believe I've heard of underground bunkers where some engineers sit during a launch, to do things like stop charging batteries right before launch.
- There is the infamous "Rubber Room", which was designed to protect astronauts and staff in the event of an emergency with a fully fueled Apollo 5. To my knowledge, this was never used during a launch, but it could have been, and was indeed very close.
- Submarines often launch orbital vehicles. The crew is presumably very close during launch.