I feel the OP description of table top gaming is a bit limited as games can be so much more than that. There are various types of strategy games, racing games, dexterity games, co-operation games, storytelling games, real time games, and so on and so on. It can be boardgames, miniature games, use cards, dice, drafting mechanics and so much more.
Table top gaming has actually become a regular hobby of mine after discovering the existence of such a gaming club in my town. I joined a little over a year ago and have started building up a game collection, partly from discovering games at club meetings and table top videos on the web, and partly from giving word of mouth or unfamiliar games a shot. I'm even working on making myself a proper gaming table for when I invite friends over.
What I really enjoy about table top gaming is the direct way we interact with one another. Sure, you can play with friends on a console, but then you are all just staring at a screen and barely giving each other a glance. With table top gaming there's much more direct interaction, through trading, attacking, scheming, etc. It's a great way of getting to know new people, breaking the ice and at the same time introducing you to a new fun game.
Some games that I play on a regular basis are various versions of Settlers of Catan (Cities & Knights is my favourite expansion), Smallworld, Lords of Waterdeep, Bora Bora, Pandemic, Ticket to Ride, Carcassonne, Stone Age, Tzolk'in, Kingdom Builder, Terra Mystica.
Some games I really hope to play more include Archipelago, Jamaica, Battlestar Galactica, Nexus Ops. There are also a ton of games being brought in that I can't currently remember the name of, but some of them are also games I want to play again.
My favourite mechanics are Worker Placement and Resource Management, I also enjoy the occasional Co-op type game. I'm not fond of Deckbuilding, like Dominion or Thunderstone, but Dice building I'm fine with. I don't like it when games get so overcomplicated that everything gets so chaotic that no one knows what to do. There was one game we played, where no matter how much we consulted the rules it was uncertain how it was even possible for one side to win the game. I'm fine with there being a lot to keep track of, and if that means you can apply a variety of strategies to win the game, even better, but when it ends up standing in the way of actually playing through a game, then I get annoyed.