My characters do everything there is to do in Skyrim. They also get all dragon priest masks. They work on getting every shout. They go into every cave they come across. They join every faction. They help every NPC. Their role is to be a person who lives in Skyrim. That's all.
They buy training whenever and wherever they can. They smith to 100 and go legendary pretty fast. Same with Alchemy.
I decide beforehand what offensive and defensive strengths I want, but it always includes archery. In either one-handed or two handed, I choose my type of weapon (sword, mace, war axe, etc) and only put perks on that weapon. I choose heavy or light armor and stick to it. I've never played full mage but I use destruction and conjuration a lot and put perks in destruction, but not conjuration, because it seems like all you need for that is magica. I use a lot of alteration to transmute ore, which helps with leveling quite a bit.
When you play like that, you level up frequently. Just recently, I found Pantea's flute, and leveled up right before I returned to the Bard's college. Turning that flute over, you of course get lots of perks, and then I turned around and bought speech training from what's his name at the college. I walked out of the building 3/4 of the way to the next level! That's almost a whole level in 5 minutes time. And, if I were at level 20 instead of 54, I probably would have easily gained more than a whole level.
One time, after the war, I went into an enemy camp, and killed everyone except the camp commander, who can't die. So I got out my shield and let him bang on it for 3 whole levels! That took about 20 minutes. You can also level up on destruction and restoration doing that. It's fun, teasing that guy until he's huffing and puffing.
Also, my current character joined the Dawnguard right at level 10, having done very little at all since Helgen, and she stuck with the entire storyline to the end. Emerged from Dawnguard at level 41, and had all of Skyrim yet to conquer!
Defeating Miraak and getting Waking Dreams helps you adjust your perk placements. I do that a lot, for example, when I want smithing, alchemy, and enchanting at 100 and don't want to go legendary, I'll trade perks from one to the other.
I play on Xbox and don't use exploits or mods. Anyway, long story short, just live in Skyrim. Don't look at it as a quest driven task that you have to finish.