Searching for my Holy Grail?

Hello out there.  This is my first post!  I am interested in purchasing a used bike that is reasonably fuel efficient, has a nice smooth engine (have prostate trouble and must have smooth), and can pull a Velorex side car.  My wife and I plan to take day and perhaps weekend trips and will travel on local and secondary highways for the most part.  I would also like to have shaft drive, a reasonable sized gas tank with a fuel gauge and a wide seat.  I a six feet tall.  I have looked at gas mileage figures and they are all over the map!  Any help would be greatly appreciated.  Cheers,  Dub