Enter your seed, then pick one or more biomes in the Biomes panel. Every patch of them lights up on the map while everything else fades, and the nearest ones are listed by distance from the center of the map.
Click a result to fly there, or click anywhere on the map to see which biome it is. Move the map and hit Search from here to look around a different spot, like your base.
Since 1.18 both editions generate the same overworld terrain and biomes from the same seed, so this map is right for Java and Bedrock alike. On Bedrock it matches chunks generated in 1.26.50 or newer.
Structures, ores and slime chunks are where the editions differ; see the Diamond Finder and Slime Chunk Finder for those.
Biomes are built on cubiomes, a re-implementation of Minecraft's biome generator, down to the single block, for whichever Java version you pick (Bedrock always uses the newest). I compared it against real worlds and it lines up basically everywhere, including the new 26.x biomes.
Nearest results sample every 32 blocks, the same spacing the game's /locate biome command uses, so very thin slivers can be missed.
Reference: Minecraft Biomes
Since the 1.18 Caves & Cliffs update, biomes are placed by a handful of smooth noise maps (temperature, humidity, continentalness, erosion, weirdness and depth). That is why they come in big coherent regions, why oceans sit at the edge of continents, and why the same seed gives the same biomes on Java and Bedrock.
Finding rare biomes
Mushroom fields are the rarest: they only form far out in deep ocean, often thousands of blocks from spawn. If the finder has nothing within 6,400 blocks, use Search further.
Cherry groves sit on mountain slopes and meadows. Pale gardens are small patches inside dark forest regions. Ice spikes are a rare variant of snowy plains, and eroded badlands a rare variant of badlands.
Cave biomes: deep dark, lush caves, dripstone caves
Cave biomes exist underground, so a surface map never shows them. When you pick one, the finder searches underground instead: the deep dark around Y=-40, and lush caves and dripstone caves around Y=0. The results show up as pins; dig down at a pin to reach the biome.
The deep dark is where ancient cities generate, and it tends to sit under mountains and high ground. Lush caves often have azalea trees growing above them at the surface.
Using /locate biome in game
With cheats on, /locate biome minecraft:cherry_grove gives the nearest cherry grove to where you stand, within 6,400 blocks. This finder does the same search without cheats, shows every patch at once, and lets you look around any point, not just where you are standing.
Why a biome on the map can look slightly off in game
Biomes in Minecraft are three-dimensional: the biome at the surface can differ from the one a few blocks down or up a mountain. The map shows the biome at the approximate surface height, which is what you see when you walk there. Edges can shift by a block or two.