First and foremost (to take a phrase that Fuji used in their advertisements back in the day), vintage Fuji bicycles are quality. Simply put, they were made well. The frames were not too heavy. The componentry they put on the bikes was quality too, and reliable. Along with their quality, they were affordable. By the way, Vintage Fuji refers to those that were made in Japan, when it was still a Japanese Company. This changed in the mid-90's.
They have a nice aesthetic. They look good! The logos and design put into them is very appealing to the eye. Strangers have noticed my vintage Fuji bikes when I've been out and about.
They ride well. They absorb road vibration. It just feels good to be on them.
They're fun. Hey, it's a bike! Bikes are fun (whether they say Fuji or not). But the fact that they do say Fuji makes it a bit more fun and interesting, knowing that you are riding a quality piece of craftsmanship that began its life halfway across the globe.
With that in mind, the bikes themselves are 'worldly.' The marketing gurus gave them names such as 'Bedford,' 'Cambridge III (and VI),' 'Touring Series IV,' 'Opus III,' 'Sagres,' 'Ecco,' 'Palisades,' 'Odessa,' 'Monterey,' 'Del Rey,' and I can go on and on and on..... You'll just have to take a look at classicfuji.com to see the rest.