Conjuration (Bound Bow), Archery, Light Armor, Alteration, One Handed (for close combat), Enchanting. I was thinking that I work my way up the light armor tree, while using the alteration armor spells to give me an extra boost of defense. Then use bound bow against enemies. Enchant my armor to add more bonuses for dealing more damage. Do you know if glass armor can reach the cap, without smithing? I want to take the atronach perk, and wouldn't summon anything, but only raise zombies and such. Would that work?

I don't see why not. I've often wanted to try a similar build - alteration, archery, enchanting, conjuration. Use thralls and atronachs to tank with flesh spells as a backup.

With Sneak, this build works well for me, although I do very little close combat (none, if everything works as planned).

Thanks. Although I don't plan on sneaking.

It's going to be tough without sneaking. If your opponents see you first, they'll typically come after you, which will leave you with an enemy in your face, and your flame atronach firing indiscriminately into melee.

If I were trying a necromancy archer like you're suggesting, I'd definitely go with sneaking, and poisons. One-shot the sentries, drag all the bodies into a battle area, lead the boss into the area (if necessary), and then lol from hiding as he has to face his enemies, one by one, with you sniping from the shadows.

Throw in some illusion, and he has to kill them TWICE.

Add spells like muffle and you could call it a Nightblade (magic based assassin)

Just path enemy npcs into your summon and they'll stick to them. Some shouting will probably be required, of course

Once your archery skill is high enough to take the Ranger and Quick Shot perks, an "action archer" build is a lot of fun actually. You're probably going to still want to sneak to get the upper hand in many battles, even if you don't perk sneak at all.

Bound Bow is awesome for this as well. It is currently one of the three combat options for my current Dunmer build. I'm not sure what to classify him as, but he uses bound Battleaxe as his main weapon, and archer and/or fire spells for ranged combat (depending on the situation)

I definitely agree with this, it's going to be tough without sneak. It's not impossible but it's definitely harder.

As to the OP, I would recommend getting the perk in Archery that staggers enemies 50% of the time, that perk will save you and allow you to get an extra shot off.