I would recommend searching (or asking) specifically for the groups you like, because there's simply too much out there ^^
However, if you're trying to get to know new groups or really don't care, I would recommend BTS'
Bon Voyage. It's officially a paid service from V app, but can find it subtitled elsewhere if you search for it (e.g
here). Basically BTS went on a trip without getting help from their managers/staff. It was hilarious & refreshing. Very early on already, I lost count of how many times they lost their stuff, their members, or their way.
Edit: I just looked at your profile page, and noticed we have 2 fandoms in common (BTS & Infinite).
For Infinite, I definitely recommend
Infinite Showtime. Showtime variety shows exist as well for other groups e.g EXO, EXID, & more recently Mamamoo + Gfriend, but I've heard that Infinite Showtime is arguably one of the best & most enjoyable (even if you aren't into Infinite). The only other Showtime I've seen is the EXO one, which was quite entertaining as well :)
Apparently Infinite's
Ranking King was also quite good.
Here's actually a full list of variety shows Infinite have starred in.
For BTS, I'd just like to add that they are very present on SNS and have soooo many videos on their youtube channel, which already provide (free & legal!) entertainment for hours. Click
here for their channel, and
here for the channel of their hardworking subbers!
Here is also a masterlist of variety shows they have been on.
Another program I just thought of is
Flower Boy Bromance, it's also on youtube. These are very tiny series of 4 to 5 episodes of 15 mins about celebrity friendships. L, V, Jungkook, Jooheon & N have been on there among others.