I do pretty much all my leveling in combat. That's what I play the game for, so i'll be damned if I'll spend the first half of the game beating on my own summons, or Shadowmere so i can get on with it. Other than that, it depends on the skill:
Destruction: Burn Draugr. They're weak against fire, which is the cheapest element, and XP is directly proportionate to damage dealt. That, and you're going to get to 100 before you ever run low on targets. There's not many spots on the map that aren't a quick sprint away from a cript chock full of them. Also, set your difficulty on Master, this gives them more HP, so you can do more damage, and get more XP per fight. Same with weapon, and armor skills.
Hand Weapons: The Companions. Just to get in, you have to beat on Vilkas, then you run off with his brother to fight Silver Hand, and Draugr. Oh look, Silver great/swords! See Destruction: Above. Beat on Draugr. Also gain access to Skyforge Steel blades, which do more damage to other than undead types, and a never ending pagent of radiant quests to go somewhere, and pound on things. Talk to Aela, and beat up some trolls. Try to get 1 to an inch of it's life, then go beat up it's mate while the first regenerates. You can fight the same 2 trolls for hours, if you don't let them kill you. Wearr Armor, and get some experience in that too.
Archery: Hunt, and save the hides for Smithy. Deer, and Elk respawn, and from Whiterun to the Rift is a massive plain you can never completely clear. Also, around Falkreath there's a lot of Spriggans. Kite them together, and use them to sweep the entire valley of game all the way to Riverwood. Collect the hides, then go see Alvor...
Smithing: See Archery above, then go beat on the Forsworn. All their armor is light, Leather tier, and a lot more valuable. Since the Iron Dagger Nerf patch, the XP is based on the value of the item, and you're not going to run out of foreswore before your Smithing is high enough. Most of their Redoubts have forges, workbenches, and grinding wheels, so you don't have to carry it far. Once you're up to 30, start melting down Dwemer crap, and smithing that. Light, or heavy, you can get up to Ebony, or Scaled without ever having to mine, and your Archery should be just fine. (Also, the Foresworn Bows are as good as Dwarven, only heavier, and use the Steel Smithing perk, so you can get more damage, and more experience, faster.)
Speech: I don't bother with this skill. If you do, sell all the forsworn armor you just fixed up, then buy, and sell until you're broke. Go do another hunting/killing/smithing run, and sell again... You should be able to keep this up with your other skills.
Conjuration: Bound Sword can be dual cast by any character with 1 perk, and if done in combat, levels Conjuration more than fast enough. It also gives a little experience doing damage. If you're also working 1 hand, half stack them, cast one, then the other a minute later so there's always one out, and dual wield. Bound Battleaxe, and Bow don't give the damage XP, but they work well if you're using other weapon skills.
Alteration: Detect Life. Do the Infiltrstion quest at Treva's Watch, and it's free. The more higher level NPCs you detect, hostile, or not, the faster it levels. Also very handy for any stealth based character to avoid surprizes, hunters finding game, and seeing the Sabercats first when traveling the wilderness.
Illusion: Calm. Shoot/Backstab/Bolt a bandit, Calm him, rinse, repeat. Also, muffle is like Detect Life in that the more NPCs/levels around you, the more XP, so you can just spam it in the middle of Whiterun to reach Quiet Casting the first day. While I'm on the subject you can go see Drevis, clean out the pools for some soul gems, free magicka Regeneration, and spam train any school, except for destruction in the Hall of the Elements. Just spread Calm/courage around, and muffle, it'll be done real quick.
Restoration: Uh. I hate training this. All the spells are so expensive, and finding a lot of good targets isn't always easy. Turn Draugr seems the fastest, but you'll need a lot of magicka. You can also stand in an Axe trap healing, or Ward Dragons, but almost all of these put you in harm's way and can get you killed.
Pickpocket: Sucks, I hate it.
Lockpicking: Useless skill, just learn to play the minigame, and you shouldn't need it. Break a bunch of picks on a master lock, and watch the levels roll in. Spend the perk points on something else.
Sneak: Lost Valley Redoubt, and Karthspire Camp. The former has walkways, and the latter water under the platforms you can sneak around without any chance of detection, all night long. Like Muffle, and Detect, the more NPCs not seeing you as long as you're crouched, the more experience. LVRD is closer, but Karthspire is the best spot.
Enchant: Get the Staff of Jyrik Gauldurson, spam it dry, and charge it with souls while adventuring for all the effects to Disenchant. Don't even start making stuff until you've got some decent perks invested, concentrate on Weapons, and keep them charged. Start with Soul Trap, you'll need it. I know where to get every scripted effect, the rest are random, so good luck. Do the Labrynthian for all the Absorb Stat effects, they rock, and add a lot of value. Get the Black Star ASAP, and make a special weapon that kills, and completely discharges in 1 hit.
Alchemy: Don't ask me, not interested. I can't stand this grind, out of all the ones in this game, it's the most excruciatingly tedious. I did it once, and never felt it was worth it.
Block: So slow, but so worth it. The higher level enemy, the more experience you get from blocking their attacks, and bashing them. Giants are your best bet, once you can survive them, but it's hard to get one alone, and tanking on 2 is suicidal. So kill one, and their mammoths, and dance with the last one. Keep healing handy, and use it while they recover. I usually lead with a Critical charge, and keep them off balance so he doesn't hit me. `player.setrace redguard` Adrenaline Rush. A mad minute a day of dancing with giants should keep you block up with your other skills.
of the 4th era, can bond together as one, too... 
