There are combat, magic and stealth skill trainers. Be aware they will charge you a fee to level up the relevant skill though!

Combat: Archery
Journeyman Trainer: Find Faendal in Riverwood.
Expert Trainer: Find Aela the Huntress of The Companions in Whiterun.
Master Trainer: Find Niruin of The Thieves Guild in Riften.

Combat: Block
Expert Trainer: Find Njade Stonearm of The Companions in Whiterun.
Master Trainer: Find Larak of Mor Khazgur in The Reach.Combat: Heavy Armor
Journeyman Trainer: Find Hermir Strongheart in Windhelm.
Expert Trainer: Find Gharol of Dushnikh Yal in The Reach.
Master Trainer: Find Farkas of The Companions in Whiterun.

Combat: One-Handed
Journeyman Trainer: Find Amren in Whiterun.
Expert Trainer: Find Athis of The Companions in Whiterun.
Master Trainer: Find Burguk of Dushnikh Yal in The Reach.

Combat: Smithing
Journeyman Trainer: Find Ghorza in Markarth.
Expert Trainer: Find Balimund in Riften.
Master Trainer: Find Eorlund Gray-Mane in Whiterun.

Combat: Two-Handed
Expert Trainer: Find Torbjorn Shatter-Shield in Windhelm.
Master Trainer: Find Vilkas of The Companions in Whiterun.

Magic: Alteration
Journeyman Trainer: Find Melaran in Solitude.
Expert Trainer: Find Dravynea of Kynesgrove in Eastmarch.
Master Trainer: Find Tolfdir of The College in Winterhold.

Magic: Conjuration
Journeyman Trainer: Find Runil in Falkreath.
Expert Trainer: Find Phinis Gestor of The College in Winterhold.
Master Trainer: Find Falion in Morthal.

Magic: Destruction
Journeyman Trainer: Find Wuunferth the Unliving in Windhelm.
Expert Trainer: Find Sybille Stentor in Solitude.
Master Trainer: Find Faralda of The College in Winterhold.

Magic: Enchanting
Expert Trainer: Find Sergius Turrianus of The College in Winterhold.
Master Trainer: Find Hamal in Markarth.

Magic: Illusion
Expert Trainer: Find Atub in Largoshbur in The Rift.
Master Trainer: Find Drevis Neloren of The College in Winterhold.

Magic: Restoration
Expert Trainer: Find Keeper Carcette at The Hall Of The Vigilant and Colette Marence of The College in Winterhold.
Master Trainer: Find Danica Pure-Spring in Whiterun.

Stealth: Alchemy
Journeyman Trainer: Find Lami in Morthal.
Expert Trainer: Find Arcadia in Whiterun.
Master Trainer: Find Babette in The Dark Brotherhood Sanctuary.

Stealth: Light Armor
Journeyman Trainer: Find Scouts-Many-Marshes in Whiterun.
Expert Trainer: Find Grelka in Riften.
Master Trainer: Find Mazir in the Dark Brotherhood Sanctuary.

Stealth: Lockpicking
Expert Trainer: Find Majhad at Khajiit Caravans.
Master Trainer: Find Vex of The Thieves Guild in Riften.

Stealth: Pickpocketing
Journeyman Trainer: Find Ahkari at Khajiit Caravans.
Expert Trainer: Find Silda the Unseen in Windhelm.
Master Trainer: Find Vipir of The Thieves Guild in Riften.

Stealth: Sneak
Journeyman Trainer: Find Khayla at Khajiit Caravans.
Expert Trainer: Find Garvey in Markarth.
Master Trainer: Find Delven Mallory of The Thieves Guild in Riften.

Stealth: Speech
Journeyman Trainer: Find Revyn Sadri in Windhelm and Dro'marash at Khajiit Caravans.
Expert Trainer: Find Ogmund the Skald in Markarth.
Master Trainer: Find Geraud Gemaine of Bards' College in Solitude.