Hive is really fun. Each game is pretty short, which gives you a chance to try more than one strategy in one sitting. We only have the base game, and it doesn't feel lacking.
Roll-and-draw games are pretty fun too; they're almost like Tetris combined with Scrabble. We have Railroad Ink; Steve Jackson games publishes a dungeon-crawl-themed one that looked like fun, though the reviews I watched generally preferred Railroad Ink between the two.
Now that I think about it, the game we've played the most, and had the most fun playing, is Sushi-Go-Party. I didn't expect to enjoy it, because it involves a shuffled deck of cards, but it's very well designed (i.e. you do have to use your brain to win). We have the big box version, and I'd recommend it over the original. Both are good (the original is just a subset), but the big box has more deck options, and they're worth it.
For reference, our gaming group is me, my wife, and our seven year old girl. She's enjoyed all three games, but Sushi-Go-Party is definitely her favorite.