If you're looking to brew your own, it's definitely a learning process, but can be a lot of fun.
This post ended up getting pretty long, but hopefully I managed to keep it organized enough to be useful
Concept
You'll want to start with a basic concept. "A cave populated with kobolds" is always a good one, since the little buggers love traps. "An ancient tomb that's recently been penetrated by graverobbers" is also a classic, allowing for all sorts of traps and puzzles.
The real classic modules, like Caves of Chaos and the Temple of Elemental Evil, tend to have large dungeons with several factions. I wouldn't jump in on that until you feel confident.
Map
In both our examples, the current use of the dungeon isn't it's original purpose (it's a natural formation or a resting place, not a looting place). This is nice, because it lets you start with a map and the rooms' original functions. The best advice I can give for designing the physical layout is to make sure there are multiple entrances into the dungeon and loops among the rooms. For more, I'd point you towards The Alexandrian's articles on what he calls
Jaquaying.
For a small dungeon, I'd only include maybe half a dozen rooms. If you're feeling confident, include a second layer below the first. Maybe the caves extend along an underground river into deeper reaches or the tomb is built atop the graves of an even older civilization. Try to include multiple ways to move between the layers, maybe there's a sinkhole in one room or an entrance from the surface to the second layer (maybe it's well hidden and no-one knows about it).
Caves usually follow the flow of water, so a stream or river is a great feature. In a fantastic setting, it could also be burrowed out by something like a bulette or purple worm, giving a different feel. If you go for the burrow, be sure to mention claw marks or how the tunnels are strangely circular, so players might realize that something dug them (and not want to fight it, at all). You can mix these too, giving you something interesting to mention to the players as they switch tunnels.
The tomb will probably have some sort of main entryway, servants' tombs, shrines to the god of death and whatever gods the interred worshipped, possibly family crypts or even crypts for favored pets, probably a false crypt with a little treasure to deter graverobbers, and the actual hidden crypt with the real loot. There might even be a shaft to the surface (or so deep to connect to "the underworld"), for the souls of the dead to move on through.
Don't finalize your map quite yet, because the current inhabitants might have modified it. Just make a note of what was there. This is especially important in built structures so you can give good descriptions.
Moving to Now
Okay, so you've got your cave or tomb mapped out. Start from the entrances, both above and below. This is where the inhabitants will also have come through originally and where their defenses will be centered.
Kobolds
In a kobold cave, there'll be traps at the entrances to kobold territory... probably pit traps and rockfalls. They'd dig small tunnels (add those to the map) that kobolds can run through but humans would have to crawl, that they use to stage attacks with thrown spears. Before you can get to their nest, there'll be actual guards. The nest itself will probably be in the biggest cavern they can find, with extra chambers off to the side (natural or dug) for their chieftain and eggs.
Think about what the kobolds do when they find out they're being attacked. They're relatively intelligent, so they'll either mass up for a big battle or flee if they have another way out. Just because you have three rooms with kobolds doesn't mean it'll be three fights. It's more likely you'll have a fight with waves unless your PCs are canny.
Also think about what they do when they're not getting attacked. If they fish from a stream on the map, mention the stench of fish in some rooms, include some spears lying by the shore. If they eat fungus, make sure there's a cavern with fungus or add it to the description of their main nest.
To mix up some of the encounters, include the kobolds' pets. Dire rats are a classic, but I have a weakness for shocker lizards. Kobolds are also often associated with dragons, so a cavern populated with a small dragon they treat as a god can be a nice touch.
Tomb
In a tomb, decide where the graverobbers have already been. Those areas will be disturbed and looted, possibly causing undead to rise. Traps will probably be triggered unless they reset themselves or the canny graverobbers rearmed them. Include whatever remains of the graverobbers (probably corpses), at the end of their time. Populate the rest of the tomb based on its original purpose, with traps in some rooms and undead/construct guardians in others. Vermin or oozes might have come in from other entrances.
The tomb gets more classic traps. Think Indiana Jones. Darts flying from walls, doors that close and lock behind you, pit traps, maybe even a giant boulder rolling down a hallway. Puzzles are also very appropriate here, but think a bit first about who the puzzles are for (are only the priests of a certain god supposed to enter? The children of the dead?) and tune the puzzles to fit them.
Designing this type of area, I usually assume that there's an unopened front door and the robbers tunneled in from above. The front door can have a puzzle that hasn't been solved (perhaps the clues are in the crypt) or a guardian that no robber has yet defeated.
Fantasy
I consider it best practices to include one random cool thing in the dungeon that isn't a trick or trap or treasure. A cavern filled with tree-sized glowing mushrooms is the classic. Old D&D had a fondness for pools that had strange magical effects on thing immersed in them.
Perhaps one of the caverns has several boulders floating in the air, drifting slowly and periodically clashing against each other. The current inhabitants have no more idea why than the players.
The tomb might have a section where the ghost of the ruler buried there holds mute court over its spectral subjects. Their bodies in the other rooms might be a threat, but the ghosts don't even acknowledge their presence.
These things remind the players that there's more to fantasy than the things that they kill and the powers their characters have being weird.
The Hook
You mentioned specifically deemphasizing the hook, which definitely works for that old school feel. Kobolds kidnap people or inhabit a cave that could be used for mining or have attacked caravans. A tombrobber's spouse wants the PCs to find out their fate or the tomb is going to get looted eventually so a historian wants it emptied out before the robbers get another chance
Treasure
Make sure there's some cool loot. You don't need a ton of magic stuff because it's low-level, but give the enemies a couple potions (probably healing potions if you don't have a divine caster) and maybe one or two permanent items. In addition to whatever coin you want to give out, include a couple of objects that are more interesting, like jewelry you can describe in a bit more detail or kegs of alcohol for the PCs to sell or enjoy.
Make sure there's at least one thing in the treasure with a story. This can be as simple as someone's heirloom from town, giving a hook back, or might be as complicated as a mysterious key that it turns out unlocks a gate in the distant mountains. Treasure can be both a reward and tie in to other adventures.
Some treasure is a good hook because it's big. Maybe the caves have veins of mineral in the wall, so the party can sell the claim or start up a mining operation. The tomb might very easily have sarcophagi, statues, pillars, or even entire walls decorated with precious materials or valuable for artistic reasons, but they weight hundreds of pounds or have to be somehow removed without collapsing the whole tomb.
Wrapping Up
Okay, so you've got a map with a bunch of entrances and interesting connections between rooms. You have denizens that act reasonably when threatened and some cool traps mapped out. The treasure is set. You're almost ready to go.
The last thing I do is go through and make notes about the connections between rooms and what's obvious about them. This might seem weird, but you'll need to be able to describe the doors or tunnels in detail so the players can make actual choices. So, if a tunnel isn't used, it's dusty or covered in bat guano. If it's used, you can see its well worn. If the room it leads to is lit or has a strong scent, you can probably tell before setting foot in it.
Cheers!
Kinak