They are also a great way to liven up lots and make visiting them different each time depending on which club shows up.
Moral rivalries.
E.G. You could have a Bar that is frequented by Cops (sims in the Detective career), and have a roaming club of Troublemakers (Criminals, or Mean/Evil/Hot-headed bullies) that could show up at any Bar. Making the two clubs rivals could mean a a barfight breaks out if the Troublemakers show up at the Cop Bar one night.
Other moral rivalries could be political or religious groups, kleptos vs. retailers, promiscuous vs. prudes etc.
Sports rivalries.
Cities might have basketballs, football (soccer), American football, swimming or various other sports clubs. They, in turn, have fan clubs. E.G. The Foxbury and Britechester football (soccer) teams form Team Clubs and give each team a Fan Club. The fan clubs would be friendly with their own team, and rivals to the other team and their fans. Teams would be rivals of each other, and friendly to their fans. Set them all to meet at Pepper's Pub. Depending on which clubs spawn at any one time, it could be a brawl or a party. There are lots of sports strips/jerseys that could be used as club and fan uniforms.
Teen cliques.
Mean Girls or other teen movies inspire these. You could have the trendy/popular/socialite sims, the nerdy/geeky/techy sims, the disenfranchised/rebellious sims, the hippy/eco warrior/activist sims, the sporty/jock/gym bro sims, the arty/crafter sims, music lover/bandie sims. Each club would hang out in different lot types and interact with the other cliques and non-Teen clubs in different ways. The Gym Bros might get along with any of sports teams or sports fans, but be dismissive of/mean to creative or nerdy clubs, for example.
Co-worker socials and networking.
Befriending co-workers increases work performance. It's also common for workplaces to have staff outings and parties. For WFH style jobs it's also fun to set up a common workspace, or meet at an appropriate venue type. It's also a good way to see appropriate sims at those lots while rotated away. Careers might also overlap, network-wise. E.G. Freelance Programmers might meet up at an Internet Café to keep the caffeine coming while they code. Such a venue might also attract sims in the Tech Guru, Social Media, Food Critic, Secret Agent or Oracle (cybercriminal) career, uni students on the eSports Team or completing Computer Science degrees, teens in the Computer Club after school activity or the local Coffee Addicts or Foodie meet up. Great for storytelling about how sims met.
Clientele diversity.
You can vary the clientele that shows at various venues to make them more unique from each other. You might want sims to stick to their local venues when going out. Have them join a group with other locals and make their hangout the local venues that suit their interests, such as having all the Active sims that live in Oasis Springs hang out at the Gym in that town, or all the students in Britechester drink at that Bar. You might want sims with particular taste in music to show up to a venue that plays that music (E.G. sims who Like Blues would enjoy hanging out at The Blue Velvet, but sims that Dislike Blues would hate going there and avoid it). Make the visitors you want to see there into Clubs to give each place more character beyond the build itself.
Wealth/Class/Fame divides.
The areas in game tend to fall into different cost brackets with some being poorer/starter areas through to others being richer/late game areas. Venues could also be given the same distinction by having clubs with wealth and/or fame filters either allowed or disallowed via club doors or lock mods. You might have a fancy, country club style Rec Centre in the rich hills of Del Sol Valley, or a run down community centre style one in the Spice Market of San Myshuno. Obviously the sims that might show up to these places wouldn't be the same, so using clubs to send in specific groups of sims will make the visiting sims more believable.
Activities and added autonomy.
Another way to enliven venues and make them different from each other is to theme them around specific activities. However every Museum, for example, has the same requirements and autonomy tied only to those requirements. What if I wanted a Science/Space/Natural History Museum instead of one that functions like an art gallery? Well clubs come in handy here too. Sims would likely view space prints and possibly some collectibles as viewing things is part of Museum autonomy, but if you wanted to have interactive exhibits then they would likely not be used by NPCs. Having an Astronaut/Rocket Science club going on rocket missions, building/upgrading rockets, Botanists/Geologists analysing samples, Astronomers using telescopes, Roboticists tinkering and building Servos or an Amateur Scientists club doing all of the above would mean items that generally wouldn't be used on that lot type are actually in use making the whole lot more interesting to visit. It also makes it a likely place to meet sims with the associated hobbies or careers, if you are looking for that kind of thing in friends or lovers.