Villages on top of sulfur caves
Java Edition 26.3. Checked with Seeder's engine on .
A village to sleep in, and the 26.2 sulfur caves right below it. Your first mine is just a short dig from your first bed.
Every village in this list is directly over a sulfur cave. The maps are shown at Y = 0, where the caves are, with the village marked on top.

1 A plains village over sulfur caves, 93 blocks south-east of spawn.
Seed244773005486829
What X, Z Distance VillagePlains village 48, 80 93 blocks Sulfur Caves 46, 74 87 blocks Ruined Portal 0, 0 0 blocks Trial Chamber 48, 96 107 blocks Shipwreck 208, 112 236 blocks Stronghold -1436, 276 1.5k blocks Spawn in a plains at 0, 0, around Y 68.

2 A taiga village over sulfur caves, 144 blocks east of spawn.
Seed442860251699944
What X, Z Distance VillageTaiga village 144, 0 144 blocks Sulfur Caves -2, -2 3 blocks Trial Chamber 96, 128 160 blocks Igloo -160, 224 275 blocks Abandoned Camp 32, 304 306 blocks Stronghold -1324, -476 1.4k blocks Spawn in a windswept forest at 0, 0, around Y 85.

3 A taiga village over sulfur caves, 148 blocks south-east of spawn.
Seed442860251699945
What X, Z Distance VillageTaiga village 128, 96 148 blocks Sulfur Caves 74, 62 85 blocks Trail Ruin 96, 0 80 blocks Ruined PortalUndergroundAir pocket 304, 64 295 blocks Trial Chamber 288, 224 352 blocks Abandoned Camp -240, -256 362 blocks Stronghold 1172, -748 1.4k blocks Spawn in a giant spruce taiga at 16, 0, around Y 65.

4 A plains village over sulfur caves, 200 blocks north-east of spawn.
Seed1429451576662801
What X, Z Distance VillagePlains village 96, -176 200 blocks Sulfur Caves -2, -2 3 blocks Abandoned Camp 32, 304 306 blocks Trial Chamber -336, 48 339 blocks Ruined PortalUndergroundAir pocket 80, 368 377 blocks Stronghold -28, 1364 1.4k blocks Spawn in a windswept hills at 0, 0, around Y 87.

5 A savanna village over sulfur caves, 129 blocks north-west of spawn.
Seed308628722620600
What X, Z Distance VillageSavanna village -144, -272 129 blocks Sulfur Caves -82, -162 3 blocks Shipwreck -80, 80 240 blocks Trial Chamber 16, 64 244 blocks Abandoned Camp -176, 192 365 blocks Stronghold 1876, 4 2.0k blocks Spawn in a savanna at -80, -160, around Y 74.

6 A snowy village over sulfur caves, 279 blocks west of spawn.
Seed2550018009398761
What X, Z Distance VillageSnowy village -272, 64 279 blocks Sulfur Caves 2, -2 3 blocks Igloo 48, 16 51 blocks Ruined PortalGiant 128, 16 129 blocks Trial Chamber 112, 80 138 blocks Shipwreck 112, 272 294 blocks Outpost -224, 272 352 blocks Stronghold 1556, -412 1.6k blocks Spawn in snowy plains at 0, 0, around Y 66.

7 A plains village over sulfur caves, 58 blocks south-east of spawn.
Seed3074086031640167
What X, Z Distance VillagePlains village 0, 96 58 blocks Sulfur Caves 2, 78 45 blocks Trial Chamber 16, 128 93 blocks ShipwreckBeached 80, 272 250 blocks Ruined PortalOcean portal -432, 32 400 blocks Stronghold 1092, -1260 1.7k blocks Spawn in a beach at -32, 48, around Y 66.

8 A plains village over sulfur caves, 160 blocks south-west of spawn.
Seed5133991228066333
What X, Z Distance VillagePlains village -144, 48 160 blocks Sulfur Caves -18, -50 3 blocks Trial Chamber 16, 64 116 blocks Abandoned Camp -240, -144 244 blocks Outpost -368, 64 369 blocks Ruined Portal 304, 192 400 blocks Stronghold -204, -1916 1.9k blocks Spawn in a forest at -16, -48, around Y 69.

9 A desert village over sulfur caves, 158 blocks north-east of spawn.
Seed871578676041918
What X, Z Distance VillageDesert village 64, -144 158 blocks Sulfur Caves 2, -6 6 blocks Ruined PortalDesert portal 0, 64 64 blocks Shipwreck 256, 80 268 blocks Trial Chamber -272, 16 272 blocks Desert Pyramid -240, 288 375 blocks Stronghold -860, 1444 1.7k blocks Spawn in a desert at 0, 0, around Y 72.

10 A plains village over sulfur caves, 172 blocks west of spawn.
Seed5122454561084229
What X, Z Distance VillagePlains village -160, 208 172 blocks Sulfur Caves -90, 190 101 blocks Ruined PortalSwamp portal 64, 208 91 blocks Shipwreck -112, 64 138 blocks Monument 64, -112 264 blocks Trial Chamber 336, 320 379 blocks Stronghold 1140, 1460 1.7k blocks Spawn in a dappled forest at 0, 144, around Y 63.
Need more?
These ten seeds are the best out of thousands I searched. Seeder can find as many as you like, given the right premises, with your own range and in your favourite version.
Search in the finderGood to know
- Dig down from the village to around Y = 0 and you should break into the cave.
Questions
What are sulfur caves?
An underground biome from the 26.2 drop. Minecraft Wiki
What's inside a sulfur cave?
Sulfur cubes and cinnabar.