Once you’ve cleaned out the tower of bandits and loot, cross over the bridge. If you happen to be through here with Delphine on your way to a dragon sighting, she will stop with this and you’ll have to catch up to her if you’d like to scour the North tower.
The North tower is considerably shorter and less populated. The lowest floor doesn’t have anyone in it, so grab anything you really like (being careful of the spiked-ball trap attached to the chest) and climb the stairs. The second floor of the tower holds an unusual but nasty trap- outside the door is an iron ore vein, and a mining pick waits on the drawers here beside a potion. It’s tempting to dig out the ore, but a third bandit archer is waiting a short distance away on the mountainside, and will fill you with fletching if you stop to dig- instead, sneak or rush outside and flatten the ambusher.
Ignore the ore for now (unless you like getting jumped), and instead head up the tower another floor. Here, you can find a more heavily-armored bandit, often using an alchemy table. If they aren’t, wait until they are- you can then sneak attack them and usually wipe them out before an alarm can sound. This may briefly get the attention of the bandit chief a couple of floors up, so retreat a bit and wait for the chief to get bored and start wandering back upstairs.
The bandit chief is slightly less heavily armored than the alchemical bandit, but usually totes a magic staff (Staff of Frost, for instance) that is used with abandon. Use your best poisons or special powers to ease this fight, including Shouts as you’ve already killed off all the rest of the bandits. Make sure you don’t let the terrain trap you either- cramped towers are a terrible place to be when dealing with a high-power opponent, since you can easily misstep and fall to your doom, or get caught in a corner and beaten to a pulp. On the upside, if you can rush upstairs fast enough, you can lure the chief up there and shove -them- off instead. Once the chief is flattened, you are safe to loot the rest of the North tower.
The chest on the next floor up, under the stairs to the higher wooden platforms, contains Amren’s family sword and a few other valuables, and you can pick up some wine, books, and other trinkets in the chief’s living quarters. The very top platform holds a sheltered table, which usually has a few food items on it, but not much else. If you’re in need of Iron Ore, don’t forget to mine the vein on your way out, and make sure you get the alchemy bandit, any ingredients and books on that floor, and stop by the cookfire on your way out if you found useful cooking ingredients.
With Valtheim Towers cleared and Amren’s sword in hand, return to Whiterun and Amren will offer you his thanks: friendship, a discount on his One-Handed training, and one free rank of training each in One-Handed and Block.