I love dungeon crawling! I've got some tricks up my sleeve.
1. This doesn't apply to all, but to some, like Saarthal, look down. There are sometimes runes or pressure plates that insta-kill pure mages.
2. Sometimes there will be bandits within the dungeons. If so, play this to your advantage if you are unfamiliar with your surroundings- cast fear, and watch as they aggro everything. It's not only abuse, but removal- you can get a bandit out of the way while dealing with the archer. For instance, in Bleak Falls, the carrier of the Golden Claw will run into a room filled with Draugr. Or an even better example, Dustman's Cairn; Silver Hand (which drop a pretty penny) mingle with Draugr. Cast Fear/Rout, and begin the scouting expedition.
3. Draugr are weak coming out of their burial stones. For stealth characters, an arrow in the face gets them then and there. For melees, you can stagger them to shit here. For mages, slow them then turn them to dust. Always go for the throat in these weak time frames.
Carry a silver weapon:-
A +20 damage to undead means a minimum of 29 damage per strike with a standard silver sword even at the lowest levels.
Fire is your friend, draugr have either a 25 - 50% weakness to fire (not 100% sure on the number, think its 50).
A silver sword enchanted with a pathetic 10 fire damage is capable of 45+burning damage per strike!
Thats like rapid fire fireballs to their undead faces...
Carry a flame enchanted silver greatsword and it's a blood dust-fest!