Chances are you can pick up a (hunting rifle) scope at the 188 Trading Post on your way into Vegas (cheaper than Gun Runners anyway!)
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according to the Fallout wikia page, there's not that many places to get one.
If the hunting rifle isn't your cup of tea, the laser rifle scope can be found at a variety of places - Novac, Crimson Caravan's camp, or the Silver Rush in Freeside (to name a few): Laser Rifle scope .
All of these locations are potentially visitable in your early game.
Also, this search result is invaluable if you are looking for scopes for anything that shoots.
gaming.stackexchange.com/users/1425/Matthew Iselin
I got lucky in mine and picked up a varmint rifle night scope from the shopkeeper in Goodsprings on my first playthrough, so the potential is there right off the bat.
(Just steal some stuff and sell it to get the caps to buy it).
As for weapons with built in scope, sniper rifles don't' show up at gun runners until level 12ish I believe.
gaming.stackexchange.com/users/3917/l I
I don't know your definition of "early" but I maxed out lockpicking first (90 + manual) to get the gobi campaign rifle as soon as possible since its probably the best sniper rifle in the game.
Everything else is noise getting to that rifle until much later on when you get very good energy weapons
gaming.stackexchange.com/users/1965/Eric
I thought that the Gobi was great until I figured out that the stats are only a couple DAM points better than a standard sniper rifle.
So, on my last playthrough, I kept checking Gun Runners for a sniper rifle, a carbon fiber kit, and... a suppressor!
Now I have a gun which is only slightly inferior to the Gobi (one less round in the magazine), but helps me stay hidden longer while sniping.
(Of course, my companions often ruin this anyway, but I want them around as pack mules.)
Until I can put together the modded sniper rifle, I make do with a similar setup on a varmint rifle, providing I can get extended mags and a suppressor for one.
But Broc Flower Cave isn't to hard to get to early in the game, and only has giant rats guarding it (or RUS's, if you take the Wild Wasteland perk), which can net you the Ratslayer variant varmint rifle pretty early.
If you take your time for headshots while crouched with it, it can be quite effective.
gaming.stackexchange.com/users/1109/David Krider
Most times I play Fallout: New Vegas
I make a bee-line towards Broc Flower Cave ( http://goo.gl/rKTGUd ) to get "Ratslayer".
It's a highly modified Varmint Rifle so ammo and repair parts are cheap and plentiful.
It's got a very high critical hit rating and serves me well right into the higher levels.
More info: http://fallout.wikia.com/wiki/Ratslayer
A word of warning - if you take the "Wild Wasteland" perk Broc Flower Cave will be inhabited by giant giant rats which are very hard to kill at low levels.
gaming.stackexchange.com/users/11319/BaronGrivet
If you plan your path carefully and learn, through trial and error, the terrain you can reach the ycs/186 gauss rifle at level 3-4 but will have trouble keeping ammo for it without scrounger and the hidden valley bunker/BoS reward ammo crate (vigilant recycler is optional since the ammo crate reward/scrounger is so effective).
gaming.stackexchange.com/users/52806/Mictlantecuhtli
I found a second unique sniper inside the lot in Novac, right in the dumpster.
You need the Wild Waster perk, sometimes it pops up.
If not, you did something to your storyline.
75 damage, critical hit x5, 106 damage per second or shot, so it is fast.
It is just like the bozar from Fallout 2.
gaming.stackexchange.com/users/62627/user62627
This is my second play through of New Vegas and somehow I don't remember where I got the scoped guns I had before from. The only scoped gun I remember is a Guass Rifle which I only got because of the fight with the Brotherhood with Veronica. (which I probably only survived at the time because I had the Pulse Gun)   Where can you find a scoped rifle? Also, I keep checking stores such as Gun Runners but they never have a scope attachment(except for pistol scopes sometimes)
Where can you find a scoped rifle early on in New Vegas?
gaming.stackexchange.com
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gaming.stackexchange.com/questions/15630
gaming.stackexchange.com/users/138/Earlz
Pick up a rifle at the 188 Trading Post. You can also get the Ratslayer variant from Broc flower cave. The trading post or Broc Flower cave are the best places to look for it
There are not that many answers to this, but users suggest that the Trading post or Broc Flower Cave could be good places to search.