In vanilla, the only reason to really stay outside is to better see where you need to light things up that you don't want to be dark.
For modded, check out the Astral Sorcery mod (it's a magic mod with a little bit of a tech feel). While it doesn't exactly force you to do everything at night, pretty much the entire mod is designed around doing stuff at night.
Roots mod for 1.11+ (what I refer to as Roots 2) has a structure that does a thing (it's fairly small, but it's pretty cool) only at night or during a full moon (I forget which, but it's definitely occuring at night either way.) The mod overall doesn't really do anything special as far as time goes, however.
Getting Ender Pearls, find a nice desert or savanna or something where you can see the mobs at a distance so you can choose your fights and hunt Endermen, unless you're well geared build a 4X4 or so 2 high roof to stand under near them, look them straight in the eye and they'll come running to be slaughtered. Then only look and hit at their feet so they don't teleport away.