In Hearthome City, just outside the Pokémon Center, there is a man who cannot remember who he is. Calling himself Mr. E Goods, he will give you items for your Secret Base if you do certain tasks. Many of these tasks are easy and are well worth doing, you may even have done a few by the time you actually speak to him. These are all perfect to kit out your secret base. Below are the items you get as well as how to get them

Reward Task
Globe (Identical to the one in the GTS) Connect to the Nintendo Wi-Fi Connection
Gym Statue Defeat all 8 Gyms
Contest Cups
Beauty Cup Defeat the Beauty Master Rank Super Contest
Cool Cup Defeat the Cool Master Rank Super Contest
Cute Cup Defeat the Cute Master Rank Super Contest
Smart Cup Defeat the Smart Master Rank Super Contest
Tough Cup Defeat the Tough Master Rank Super Contest
Blue Crystal Meet 100 People Underground
Pink Crystal Give 100 Items to People Underground
Red Crystal Dig up 100 Fossils Underground
Yellow Crystal Trap 100 People Underground
Tower Trophies
Bronze Trophy Get a Streak of 10 Trainers in the Battle Tower
Silver Trophy Get a Streak of 50 Trainers in the Battle Tower
Gold Trophy Get a Streak of 100 Trainers in the Battle Tower