When I'm creating a culture, I like to ask myself what they do for entertainment. I think that it speaks volumes about a people, and yet it's heavily culturally influenced, which makes it an excellent step for getting inside the characters' heads, and the cultures' mindset.
You have to consider what the culture values. Storytelling is the sharing of an experience. The stories that a culture tells unite them, create a common reference and language, and often either foster a sense of belonging or a sense of alienation. So, in knowing what stories the culture tells, you begin to understand what the culture values.
Are their stories filled with underdogs who triumph despite the odds? Or are their stories filled with heroes/ines that would have fallen flat on their faces if not for love? Or perhaps they tell about the triumph of their culture over another? Each of these says different things about the basic perspective and mindset of the people within the culture. Stories are told at a young age, they begin to sink in and inform the ideals in childhood, and we all know how hard those childhood lessons are to shake!
Storytelling isn't the only means of entertainment, however. What other forms do their entertainments take? Are they an old, somewhat extravagant culture with access to a lot of different types of entertainment? Or are they a ritualized culture with set means of entertainment? Some cultures like opera while others like prefer sporting events and competitive games. Are your characters more likely to go to a play or to find themselves in the middle of a tournament? Are these different entertainments meant for different levels of society?
Gambling is another entertainment to consider, and one which can be particularly divided by class. The upper class may have established clubs, while the lower classes gather in a back alley around a couple of chickens. While the club may be the perfect place for you character to gather information about the upper classes, they're probably a lot more likely to learn about some things in the back alley.
Music is another big consideration, and one that can add a lot of variety to a culture. Don't think about the bard in the tavern; think about the soldiers around the campfire, or the quartet employed for a ball. Think about your average farmer and their family, on the long drive to the market. I know I always like music on a road trip! Do they sing? Is what they sing inherently different? Do the soldiers around the campfire sing about the wars their people have won? Or do they sing about home? Do the farmers sing about their daily lives, or do they sing about adventure and far off places?
There are also entertainments (of all sorts) which aren't always legal. Gambling may be one of those, but fantasy cultures don't have to conform to our culture's values, and many wouldn't. Whether your culture is more permissive or less so can communicate a lot to the reader. If they allow things like gambling, drug-use or prostitution, but outlaw the singing of certain songs or ban certain books or plays, they must consider the ideas in those songs, books or plays more dangerous. Why is that? What does it say about your culture?
How well does your culture deal with satire? Not just the government, but the people themselves? What would be considered "subversive" or "deviant" entertainment? When the rebels, rabble-rousers, and misfits go out with their friends, when they gather together just to be among like minds, what do they do for entertainment?
And consider also that most cultures have something that is theirs, some form of entertainment that is almost synonymous with the culture, even if it's practiced to some degree in other places. Are your characters more likely to walk through the market and see a puppet show or to hear rabble-rousers holding court in the public squares? Where do your characters go when they have time to waste? Where do they go when they're out with their friends?