The best place to evolve is on Route 14 because it rains there often. If it is not raining just wait around for a bit, it wont take long before it starts raining.
As for actually evolving, Sligoo can first evolve at level 50 so when you get to at least level 49, get it as close to leveling up as possible and then battle the Pokemon on Route 14 until you level up and then you will evolve.
The reason you should get as close to leveling up as possible is because the Pokemon there won't give much exp. to a level 49+