The Royale has always been one of my favourite episodes; not only of season two, but of the entire STTNG run itself. It is true that the story and the events that take place are not the most spectacular in comparison to the "top" moments of the show (eg. Borg) but nonetheless I found the story to be both intriguing and comic since my first viewing, and strengthened with each subsequent one.
I've always found the idea of past Earth relics or people, rediscovered in the current 24th century setting to be extremely interesting and engaging; if done correctly. "The Neutral Zone" from season one of STTNG is a prime of example of the idea being done wrong, while "The 37's" from season two of ST:Voyager is a great example of it being done correctly. In The Royale the one remaining astronought is already deceased so the episode does not have to concern itself with mapping out how the person would react and interact with the places and people of a time so far different from the one he came from; an issue that is one of the hardest to map out correctly or convincingly. Instead we get a journal entry from the person that serves as both a bit of story explanation, as well as gets across enough of the basic person's feelings and thoughts to give the viewer a convincing idea of the percieved hopelessness of his situation and in turn what the away team is in store for if they do not solve their current dilemma.
As is mentioned in the episode itself, the sub-story within the Hotel Royale, is a bit over the top and tacky. The viewer is far more interested in the imprisonment of the away team and their investigation and attempted solutions, than in the love affair between the bell boy and the gangster. The fact that the bell boy eats lead does little to peak the interest level up a notch either. Worf using his phaser on the various parts of the hotel in the hopes of creating an exit, Data's socially clusmy attempts at gathering intel from the hotel's inhabitants and Riker's questioning of the desk clerk are far more interesting. With Data we are also given the comic moment of him coming between the young clueless woman and the shark Texan gambler who is trying to shyster her out of her money.
The ending and solution to the episode is nothing extradordinary in it's cleverness, but it is again something that has always stuck with me since I first saw it. It's great to see Data physically crush the dice to load them in their favour. Again, it is the overall the journey to the end of the episode and the various little things that make up that journey that make this episode an extremely enjoyable one. An endlessly revolving door to nowhere, the shell of an "ancient" NASA space vessel, the discovery of the crew of a voyage lost over 250 years ago, loading of the dice and others all make this a definte watch.