What to do inside? Nothing important at all.
Inside Steven's house you can't do much thing, but you can find some rocks, each one from each region. (It don't have from Gen VI)
I believe those rocks are fossils or rare rocks from the mountains.. but who knows?
Rock Tunnel -> Kanto region
Mt. Mortar -> Johto region
Mt. Pyre -> Hoenn region
Mt. Coronet -> Sinnoh region
Chargestone Cave-> Unova region
Other things you can do, is sitting in the chairs and bed. You can find at the corner of the house a collection of rare rocks and stones assembled by Steven.
Why having access since you can't do nothing?
For that, only Game Freak knows why. You can't do much thing and maybe more special missions will came and maybe one of them will be related to the Steven's house and something can happen there.