Base Race
Not much changes here. If you don't want Perception for some reason, you can switch it out for any skill that you want. If you don't want to speak Elvish, you can speak any other race that you want. If you want a +2 bonus to any non-DEX Ability Score, you can now do that. Nothing sticks out for the base race, it's now just fine for any class that you want to play as a hundreds-year-old, charm-resistant, non-sleeping person with Darkvision. It's equally good for basically every class/subclass (although Oath of Devotion Paladins after level 7 will be annoyed by having a racial feature becoming completely useless by a subclass ability).
High Elf
You don't want Elven Weapon Proficiency? Switch the weapons for any other weapon or tool proficiency that you want. Don't want to take a +1 bonus to Intelligence? Switch it out for any other ability score.
If you want to make the absolute most out of the free Wizard Cantrip, be any non-Arcane Trickster Rogue and take either Booming Blade or Green Flame Blade. So long as you are a Melee Rogue (so Swashbuckler or Inquisitive are really good choices), you just straight up get a damage boost over what other Rogues will be doing, and the damage scales. If you take Booming Blade, go up to an enemy that you can Sneak Attack and isn't near any of your allies, attack them, and then Disengage and move away from them. If they try to move towards you to attack, they take the damage from Booming Blade. If they stay there and don't have any ranged attacks, they're wasting their turn.
Green-Flame Blade users are best for situations where the person you're attacking has another enemy within 5 feet of them, but that enemy is also your enemy. This isn't very common, but is nice when you can get it to set off (if you're built completely around punishing two people with one attack like this, be a Phantom Rogue to stack GFB's extra fire damage with Wails from the Grave, which lets you deal 1/2 Sneak Attack necrotic damage + Spellcasting ability modifier fire damage, scaling to 4d8+Spellcasting ability modifier fire damage at level 17). It's a niche combo, but it's solid mechanically and cool.
Wood Elf
Anyone that wants a 35 foot walking speed, ability to hide while lightly obscured by natural phenomena, and the ability to switch out Elven Weapon Training benefits from this race. So, mostly Monks, Rogues, and Rangers, as was normal with this race, but also now Barbarians for the increased walking speed, and anyone else that benefits from those fairly niche abilities. So, the class-combos that used to be the most optimal with this subrace still are, but they're effective as anything else, too.
Drow (Dark Elf)
As with the Duergar, this race is now good for anyone, so long as you're fine with Sunlight Sensitivity. A thematic combo that I've seen frequently post-Tasha's that makes use of the Customize Your Origin feature is the Dark Elf Twilight Cleric of Eilistraee (which grants access to the Darkness and Fairie Fire spells for free), but that's more of a flavor combination more than an optimization one. This race gets better for spellcasters if your DM allows you to cast the innate spells with your Spell Slots, as the new spellcasting races do. And, as with the Wood and High Elf, Drow Weapon Training can benefit anyone if they switch out their redundant weapon proficiencies (if the class gets proficiency in simple and martial weapons) for proficiency with tools.
Eladrin
As with every other race and subrace in the game, you can now change your racial +1 to Charisma to any other ASI of your choice. Additionally, Fey Step is great for if you want to be able to teleport without casting Misty Step. So, an Eladrin Barbarian can teleport 1/short rest while raging, and get an additional effect. This thematically vibes well with the Storm Herald subclass, so you could be a Winter Eladrin Tundra-Storm Herald Barbarian that is resistant to cold damage, is surrounded in a mini-blizzard that protects them and their allies while raging, can freeze water that they touch, and teleport to scare enemies. Desert-Storm Heralds with Summer Eladrin allows you to have an aura of fire around you that damages enemies, gives your resistance to fire damage, lets you set objects on fire with your touch, and burn people by teleporting. It's not super effective mechanically, especially with having to give up activating your Storm Aura in order to teleport, but it is very cool thematically and would be a fun character to play.
Sea Elf
If you want to be a non-Triton version of Aquaman or Percy Jackson, this is the way to do it. Any class works for this, so long as you want to be functional in aquatic environments as your main draw to this subrace. However, aquatic subclasses will probably have many redundant features with your racial ones (like the Fathomless Warlock, a bit of the Aberrant Mind Sorcerer, some of the Storm Herald Barbarian, etc). There's not many features to synergize here, but it's a good subrace for anyone that wants to be aquatic and still functional on land-based campaigns (unlike Grung and Locathah). The best synergy I can think of is a thematic one that's slightly more effective than it was before TCoE, which is an Aquatic-themed Moon Druid that can communicate with aquatic animals, get a swimming speed for any of their Wild Shapes, and eventually be able to turn into a Water Elemental as a way of completely embodying the sea.
Shadar-Kai
Like the Eladrin, this subrace is useful for classes that want to teleport as a bonus action without casting a spell. So, Barbarians and spellcasters that cast a spell with their action and teleport as a bonus action. Thematically, the best subclasses for these are Zealot Barbarians (taking necrotic for your extra damage), Spirit/Whisper Bards, Shadow Sorcerers, Undead Warlocks, and Necromancy/Abjuration Wizards. It's also a good option for Shadow Monks, getting more teleportation abilities and damage resistance after you do at level 3.
Pallid Elf
This subrace, like the Drow and Duergar, is now beneficial to all classes that want its innate spellcasting (again, DMs that allow Hexbloods and Fairies, will probably allow spellcasting classes to use their spell slots to cast its innate spells), as well as classes that focus on Wisdom (Druids, Clerics, Rangers). However, even for classes that don't focus on Wisdom, perma-advantage on Investigation and Insight (and a +5 to Passive Insight and Investigation), and innate spellcasting for the Light cantrip at level 1 and Sleep and Invisibility at later levels is nothing to sneeze at, especially for spellcasting classes that don't already have those spells on their spell lists.
Mark of Shadow Elf
Like all Dragonmarked races/subraces, this race is most effective for spellcasting classes/subclasses that don't already have their innate spells/expanded spell list on their spell lists. This subrace was, and still is, most effective for Rogues, Bards, and Warlocks, but is also useful for Rangers, Infiltrator-Armorer Artificers, and most other spellcasting class options.
