What grind are you specifically worried about? Taken King (The expansion from last year) did away with most of the grinds as far as leveling is concerned.
Rise of Iron has expanded on most of that.
I'll try to elaborate as best I can with what I can imagine you would consider the grind to be:
Leveling:
Characters can reach level 40 with a traditional XP bar. At this point in time, there are enough story missions, strikes, quests and bounties, that you should be able to hit this without really having to replay anything more than once.
Light Level:
There is a second leveling system called Light that is basically the "value" of your weapons, armor, and gear. This is more of a way to show you how you progress in the game, but you'll likely finish the story missions of the game without being quite near the Light Level cap.
The last main story mission for the latest expansion suggests you be LL (Light Level) 340. This number should be quite easy to reach and surpass.
However, around 350-370, progress slows down a little bit. Instead of seeing gear jump up by 10-20 points a pop, you'll be finding gear with 1-4 points of improvement instead.
Now, if you have no desire to do any raids, then LL doesn't matter to you. As LL is only really a tool to do the 3 activities in the game. Raiding, Iron Banner, and Trials of Osiris.
Raiding, of course, is a 6 man PvE activity.
Iron Banner is a 6v6 PvP activity that usually last a week, but only shows up about once a month.
Trials of Osiris is a 3v3 PvP activity that pops up every weekend.
These are the only game modes that Light Level matters, so if those don't mean anything to you, then the grind for Light Level doesn't really exist.
Other than these two major things, there are a handful of quests that require a certain level of grinding, but those are usually for high endgame rewards. To one of the three original exotic swords requires a large amount of grinding. To get three of the four raid exotic weapons (potentially) requires a lot of grinding.
Really, though. Bungie has gone through some pretty far lengths to remove grinding from the game. It might still pop up on occasion, but it is no where near the main proponent of the game as it once was.