I have done this a zillion times before, never without problem. I started the "Trouble in whiterun" quest, and Farkas wanted me to go intimidate Elrindir. The problem is, he seems to have vanished. When I go to the quest journal and click the show in map feature, it doesn't show where Elrindir is. there is no quest marker pointing to him either. It is like he is gone. Is there anything I can do? I have invested a lot of time into this character. I am on PC.

EDIT: And before anyone suggests it, no I do not have an earlier save to go to before I took this quest, unfortunately.

you can try to use console commandos to summon him to you. I dont remeber the commandos in my head but you can look it up

You can try typing console prid 1a681 and enter after that moveto player. If he is dead then resurrect on console too.

The console can be accessed in-game by toggling the 'tilde key' (the actual key can be ~, o, ?, |,^, \, §, 2, etc.. depending on your keyboard layout), found near the "1" and "Esc" keys on most keyboards. Target the NPC/actor, by first type prid , Enter. Then, type the command by itself.

Move an NPC to the Player: type prid 1a681, Enter. Then, type moveto player, Enter. Using this code will instantly put Elrindir next to you.

Hope this help you.

Can you be a little more specific. I have zero idea what any of that is, besides the resurrect command.

"prid" is "Pick reference by ID". Basically, you select the actor Elrindir to be the target of your next console commands. 1a681 is Elrindir's actor ID. With the prid command, you can target things without seeing them, as long as you know their ID.
"moveto player" is kind of self-explanatory.

Slightly off-topic, but it's weird that he's not in the Drunken Huntsman. I always avoid the Companions' "rough 'em up" quests, so I don't know how they work. Does the target typically go into hiding?

No, he should be where he always is. The targets don't change their schedule.