Dungeon crawls. Resources are king. Time, light, food, water, encumbrance, line of sight, sleeping in shifts, marching order, etc are what make or break a dungeon crawl. Without focusing on those, there's really no point to running a longer dungeon. Something you can do in a session or two, like a five-room dungeon, aren't what I'm talking about. Pick up an older edition of D&D (OD&D, B/X, BECMI, or AD&D) and play it straight. Everything you need is in there. Likely way more than you'd need. Pick up a free OSR module like
Tomb of the Serpent Kings. Did I mention it's free? It's free. And it's designed specifically to teach players (and DMs) how old-school dungeon crawling works.
Action resolution. Only roll if the outcome isn't obvious from the fiction and there are interesting consequences from both success and failure. Make rolls about mid-way through whatever the task is, if it's not immediate. Like climbing walls or moving silently. You're already committed to the action, you're already mid-task, then you roll for it. Encourage the players to think, plan, and outwit obstacles instead of default to picking from the menu that is their character sheet. If they can divert the river and flood the dungeon without a single roll, they deserve every copper piece they can find in that dungeon. Interacting with the environment
is the game. Don't skip that and just roll dice.
Hex crawls. Grab a map. Randomly generate points of interest. Drop in a starter town. Go.
Worlds Without Number is the single best resource for making hex crawls. Other great resources are the Hex Flower Cookbook, Azgaar's maps, Dyson Logo's maps, Dark of Hot Springs Island, Book of Challenges (3X), Dungeon Delve (4E), Keep on the Borderlands, Village of Homlet, Against the Cult of the Reptile God, The Mother of All Encounter Tables, The Mother of All Treasure Tables, Undying Sands, Five Torches Deep, Maze Rats, The Random Esoteric Creature Generator, Cairn, and so...so many more.
Absolutely stuff your hex map with interesting things to do. Make connections between the hexes and the inhabitants. This faction hates that faction because of whatever. So when the PCs blunder in they have choices to make and potential allies to win over. Wind up the PCs with promises of fortune and glory. Then set them loose and watch them bounce around the map for however long you're willing to run the thing. When they overcome something in one hex, give it a cool down timer for when something new moves in or the old thing comes back. The keep the goblins were living in won't stay empty forever. The Alexandrian has a article or series about this, I just don't remember what it's called.
Diplomacy. Great game. More people should play it.
Matt Colville has a great series on politics in RPGs. (Use those videos as a primer on building factions for hex crawls.) It's well worth the watch. Run social situations like a game of Diplomacy. It's all about the player making choices, picking the right thing to say, and coming up with a persuasive argument. Yes, this means characters are only as persuasive as their players. That's a feature, not a bug. It works the same for INT and WIS. The player will never be able to think above their INT, substituting in a roll for players thinking is a problem for me.
Mysteries. The Alexandrian's three-clue rule is fantastic. As are his articles on node-based design. I haven't seen anything that comes close much less is better than those, so I'd point people to those happily.