A well-maintained BMW K1200RS can be had for around $5k and is still a fabulous Sport Tourer.
Recently posted to Pilot Spin:
Here is the best bike I've ever owned, and still own with about 82,000 miles on her...
As delivered in 1999:
After some light cosmetic enhancements:
A more major mod, details published in the BMW MOA magazine:
And, more recently, camping at an Airhead rally near Boone, NC:
About 17 years old now, but still feels solid, planted and swoopy fast - "all of one piece", as it were. Been all over the continental US and Canada.
As an aside, I think this was close to the best BMW ever. None of their current line appeals to me, mainly due to many, many reported reliability concerns. Too bad.