It's always a strange sight to see a town that's constructed in a Soviet style. You'll see several during your trip to Mongolia and Erdenet is no exception. I was able to visit the mine (by appointment) and its museum. If you're hoping to bring back souvenirs from Mongolia, it's worth knowing that Erdenet is a centre for rug production.
The town's also a good base if you want to visit the Amarbayasgalant Monastery, AKA The 'Monastery of Tranquil Felicity', a superb building that sits on the steppe 70km to the north of town. It's primarily Chinese in style but has some Mongolian and Tibetan influences. Built in the 18th Century, it's one of only a few monasteries that managed to largely avoid the Stalinist purges and retain many of its original features.
Erdenet's main attraction is, without doubt, the huge copper mine on its outskirts. You can visit it, but not as easily as previous years, so better to check that out in advance.
As for me, as soon as I saw the town and dusty landscape I wanted to hit the road, but if you decide to stay, you'll no doubt enjoy some rewarding encounters!! You'll meet not only Mongolians but also Russians who've moved here in droves to find work.
Erdenet is a useful departure point if you're heading to the Selenga Rivervalley, a far more calming experience. 70km north of Erdenet you can catch a boat and head downstream to Hyalganat. To the west of Selengue, you'll meet its confluent, the Egg River, from where you can travel back upstream. It's a great outing into the wild that's a bit off the beaten track.