There are a few different ways to construe the term "nice." The Oxford dictionary has this as the first entry, "pleasant; agreeable; satisfactory." I agree with Whelen and the other posters here that "only accurate guns are interesting." But I construe a nice rifle to mean one that is accurate, is built to an excellent standard of fit and finish, and is well suited for its intended task.
But for a rifle to be "NICE!" I think it also has to meet a high level of aesthetic value. To me that means all the prerequisites of a nice rifle, but also one that is built with a fancy grade wood stock and well blued steel.
I shot a Winchester M70 25-06 sporter as a varmint gun. during my teens. In grad school I shot a Wby Varmintmaster 224 Wby. Because my aesthetic tastes haven't changed that much over the years, what a consider to be NICE(!) rifles are custom Weatherbys and Winchester Model 70s in SuperGrade French walnut.
People's aesthetic tastes are personal to them, so I don't expect anyone else's to match mine. But the difference to me is that a nice rifle is an excellent, highly functional piece, whereas a NICE(!) rifle is all that, but also stirs your soul - sort of like a Ferrari sports car or a Colnago racing bike.