Life in the 24th century isn't a Utopia, but compared to today it looks like it in many ways. On Earth, very few are hungry and those that are are in that state largely due to their own vices. Disease is largely eradicated, and those that still exist are (again largely) easily managed with medicines and gene therapies. Energy is plentiful, as is drinking water. The environmental disasters that loom on the horizon today, and became a reality in the late 21st Century are a thing of the past. The politics of 24th century Earth deal mostly with matters pertaining to the Concord and not between rival Terran nations. We've abandoned the machismo and arrogance of today's society because we had to as a species when we joined the galactic community. There are still wars, rogue states, spying, greed, avarice, fanaticism, and violence, but such problems rarely affect the lives of those living on Earth and its established colonies in the time of the Mythic Space campaign.
Life for most humans in the future isn't much different than it is today. Sure, energy is abundant and you don't generally have to worry about where your next meal is coming from, but there are still jobs to do and bills to be paid. Corporations are even more massive, some are virtually stellar nations in their own right. These corps are split into various subsidiaries and are bought and sold almost constantly. Most people working for these companies rarely know exactly who they are working for, and frankly most don't care as long as the credits keep getting deposited. The biggest difference is that without the need to run to the grocery store or the gas station or bother with any number of "fixer-up" jobs, people have more time to devote to their hobbies or to entertainment. This is more pronounced on established worlds. Out on the colonies of the frontier, life can be a bit more focused on survival rather than catching up on the latest vid or working on perfecting your cloud painting technique.
The forms of entertainment are wide and varied, but they still tend to boil down to a few key areas: Movies ("vids" as they are called now), Games, Music, Art, Theater, Literature, and Sports. Whenever different cultures interact, there is an inevitable blending and sharing between the two; such has been the case since humanity was a collection of various tribes and city-states and so it continues to be now that humanity is part of a cosmopolitan galactic society. Not long after the humans and fraal joined forces, fraal art and music became all the rage on Earth. Even the fraal took to certain aspects of Terran culinary techniques and fashion. These blendings between cultures only increase further the more species are introduced into the mix.
Musical interests have always been nebulous and hard to predict. That is even moreso now. The music of the 24th century isn't that much different at its core compared to today, but the influences of other cultures and the exposure to new instruments and approaches to making music certainly have their effect. Not to mention the aspect of art imitating life. What would be likened to the Country music of today deals less with tractors and big-rigs, but rather with life on the stellar frontier. Still there is the elements of love, honor, heartbreak, and having a good time that are essentially timeless and are carried through into the 24th century.
The biggest change is how mankind has embraced its place on the galactic stage. Alien artists are booked and sell out packed arenas on Earth continuously. Earth isn't any different that most other members of the Concord, and partaking in the bounties of a shared society does have it's perks. It's nothing to go hear a Klingon opera one night and then a couple days later go hear an Ithorian singer open for the latest human diva.
Sports have been blended in much the same way. Baseball, football, basketball, soccer, and hockey are still played even in the future. As more species become part of different societies, they also bring their sports with them or want to try their hand at the sports of the natives as well. There are various leagues to the "good ol' human games" throughout the Concord, though primarily in areas with larger human populations. There have been rules implemented by each league to mitigate injuries due to special circumstances of various species playing together and the prevalence of genetic modification and cybernetics. After all, it would be dangerous to play basketball with a 12 foot tall being that weighs half a ton. Sports, and gambling, are one of the main areas where humans quickly made in-roads in dealing with other species. If anything, humans love a contest. Vid sports channels on Earth and many Sol Alliance colonies carry a wide array of sports from many worlds. It's nothing to see a kid going to school with a ballcap of his favorite baseball club and the logo of his favorite alien sport team on his backpack.
Movies, television, and games are far easier to get immersed in. Virtual Reality became a reality in the early 22nd century. Holodecks followed about 50 years later. Vids are still largely shown on a 2d surface, but games are largely offered up only in VR. There are some vids, primarily sports, that are offered in VR, but few movies go to the expense to offer on that platform...except in the realms of, ahem, adult entertainment. Even the VR offerings for sports only offer choice seats, and don't allow the viewer to be in the game, unless they are playing a VR simulation.
Libraries are largely all digital. The wave we see now of moving away from physical mediums only continues in the future. The works of authors from across the Concord and beyond are available from most libraries. Plus, the digitizing of classic works from the whole of human history are available as well from most institutions. There are still libraries in the classical sense that seek to preserve the physical copies of books and scrolls, and the trade of these tomes is very active in both legal and illegal avenues. Libraries have largely merged on most worlds as getting from one side of a planet to another is nothing like it is today. It's nothing for someone living in Baton Rogue to spend and afternoon pouring over books at the Terran Library of History in New York and be back home by supper.
Art of many worlds is quite popular as well. The various art galleries in Rome, New York, Moscow house classic works of human artists to up-and-comers from the Terran colonies and members of the Concord as well. Much like the trade of literature, the sale of art is lively both legally and illegally, even moreso in most regards. The black market for antiquities both human and alien has been booming for some time now. This is one of the reasons that when ruins are discovered on alien worlds, the Concord does its best to try and protect the sites from plunderers looking to cash in on the history of a fallen species.