Age helps a lot of things, but it won't make crappy cider good. Do it right to begin with, and age will make your good cider great.
How I make hard cider that I like (your experience may vary):
1) Use ale yeast. I like S-04 and T-58 for ciders, but I've had more success with any ale yeast than any wine yeast.
2) Check and adjust pH throughout fermentation. Low pH = stressed yeast = bad flavors. Yeast is happiest in the 4-6 range. Yeast gets really grumpy under 3. Too high of a pH could open the window for infections, so I usually shoot for 4.
3) Rouse, rouse, rouse, rouse. Rousing blows off CO2 and undesirable fermentation byproducts, such as sulfur.
4) Ferment under 70*. After all that rousing you're doing in step 3, the fermentation will generate heat, which you'll need to control.
5) Stagger your nutrient additions. Add the right amount at the right time.
If you follow the above steps, I guarantee your results will be much better. I've made ciders this way that were drinkable in 2 weeks, good in 4 weeks and great in 8 weeks. I've made ciders without rigorous fermentation controls that were bad young, and only mediocre after many months.
Another thing to think about when making cider is the basic flavor/character you're trying to target. Things that affect flavor and character are pH, type of acidity (malic vs. lactic vs. citric all taste different, and you perceive their acidity differently), structure/mouthfeel (sometimes from certain wine yeasts, but mostly from things like the fruit itself or oak), perceived sweetness, alcohol content, and carbonation.
If you're starting out with store-bought apple juice, keep in mind those apples were grown to make apple juice that tastes good. They are not the same type of apple that makes good cider. Granny Smith makes a decent one-varietal cider, but most "cider" varieties of apples are extremely hard to find. Most hard cider makers blend apples too, to get the right mixture of tannin, acidity, etc. in their must.
Homebrew and winemaking stores sell all kinds of additives you can use to adjust the parameters, like selling different acids and blends, oak alternatives, tannin powders, etc.
I personally like to use Earl Grey tea for my tannins, and that gives the cider a nice floral/citrusy flavor as well.