Most of the Concordes can now be visited. The one I recommend in the UK is G-BBDG at Brooklands.
G-BBDG was one of the prototype production aircraft, later used by BA for spares. Stored at Filton, it had been cannibalised to such an extent that it looked a very sorry state when it was donated to Brooklands:
Thanks to a huge amount of hard work by an army of volunteers (some of whom had been BA Concorde engineers), it was gradually turned back into this:
The rear of the aircraft has been turned into a mini-museum, while the front cabin has been restored to the pre-crash interior.
A plasma screen and triggering of the mach-meters now provides a virtual flight experience which is about as close as you can get to the real thing until someone sticks some Concorde seats into a full-movement simulator.
I was pleased to be one of the sponsors of this work.