What is the best place to set up and use sniper rifles on "Resistance" in Spec Ops: Survival Mode?
This is a tough one to answer, mainly because it depends heavily on your strategy other than choice of weapon. I find on survival maps the best spots are those that are within easy running distance of the armories, and which provide good cover from the AH-6 overwatch choppers. They should also be areas where enemies generally approach from only one direction, if possible.
For this reason, I think one of the best places to set up shop on Resistance is inside the building in the center of the map. Lay down in the corner behind the side of the couch. From this position, you can cover the doorway to the left, as well as the ramp up from the lower level. Bullets can't penetrate the couch (I don't know how much the kevlar coating on the fabric was, but it totally paid for itself), so if you need to reload, you can lay down and take your time.
A sentry gun or two along the back wall of the room will thin the enemies out and stun them from time to time, making headshots and cleanup easier. The only tough part is the Juggernauts, and you have two "outs" from the room, and you're also close to the air support armory should you need it. Flashing them while they're in the sentry guns' kill zone will also help. Sniping from this position can be tricky though - the guys on your left are going to be super close.
If you're going for a more "long range" engagement, you might want to consider one of the second story balconies in what I call the "cafe" area of the map. There's one in particular that overlooks a long alleyway, where you can only be approached from behind. Some claymores, a Delta Squad, a sentry gun (or some combination) might at least alert you to enemies approaching from the rear while you snipe down the alleyway towards the book shop. The disadvantage here is that you're vulnerable to AH-6 fire from this position, and you're a bit vulnerable from the rear, even with support. If things go pear shaped behind you, you can always vault the end of the balcony and escape down the alley towards the book shop, or down the street towards the center building.