A little late to the party, but I'll throw in my $.02...
My riding profile was almost exactly what Curtis is talking about: weekend fun bike, and (mostly) one-up touring. Our Miata replaced our two-up bike back in 2011. I did quite a lot of track time on bikes from 2000-2006, so I'm pretty demanding in the performance department.
ST1100 - one of the best ever, I had two of them. Fantastic bikes, but getting very long in the tooth. An ST1100 was our last two-up bike.
ST1300 - very competent, but about as interesting as a Honda Accord. I don't know how Honda managed to completely eradicate everything interesting about the ST1100, but they did.
BWM air/oil cooled RS/RT - I had an R1100RSL, and this generation and the 1150 are great bikes. All day comfort and decent performance. None of the reliability problems and complexity of the later BMWs. Like the ST1100, getting long in the tooth. Very few options for replacing worn out suspension. Low mile R1150RTs are cheap and could be real gems.
Connie 14, FJR - Never owned one but have ridden a few. Great bikes, never tripped my trigger to the point where I bought one.
Now, for the top contenders...
VStrom 1k - GREAT sport touring bike. Mine was an early one (2002), and I rode it border to border and coast to coast. Corbin seat, hard bags, bunch of other farkles. Sounded fantastic with Two Bros slip ons. Terrible wind management - this is an issue with a lot of ADV bikes, which is why they have funky looking windscreens. Needed a bigger alternator, and the factory GIVI bags were WIDE. MPGs would drop into the 30s with a lot of right wrist, or headwinds and range dropped under 150.
'Busa - Really, really good bikes. Great suspension, monster engine, torque everywhere, stone reliable. I kitted mine up with hard bags, raised bars, and lowered pegs and rode the E36 M3 out of it. They do lack some 'touring' amenities - big alternator for farkles, cruise, ect. but I was surprised how good it was as a tourer. Keeping tires under it was a problem... all that torque shreds rears if you like your corner exits. Also, the riding position eventually got uncomfortable for me so I sold it for something more upright. Two up for any distance is really a non-starter.
FJ-09 - This was probably the best all-'round bike I've owned, and I've owned a lot of bikes in 40+ years of riding. Under 500lbs with hard luggage, and over 100hp. The triple 900 engine is a delight. Mine was a '15 and lacked cruise and some other amenities the newer bikes have, but it was still fantastic. It's a hooligan bike in touring clothes, but still comfortable enough for all day travel. Not as much wind protection as something like an FJR, but still not bad. Factory suspension is on the cheap side, like most bikes. Tight quarters for two-up riding.