As the guy running a MLP RP on this forum, it'd be strange if I didn't give any advice.
Firstly, don't use my RP as a guide. It isn't a nice, cheerful setting, it's full of combat and has even had some deaths. So yeah, ignore my RP.
Second, you should probably realise that while actual fighting is fairly uncommon, even in the show Equestria isn't that nice. Ponies have at various points been shown to be just as greedy, selfish, dishonest and mistrustful as your average human. There's a cut-throat fashion industry, some upper class political struggles and con artists. And that's just the ponies.
The show mostly takes place in Ponyville, which is right next to an evil, enchanted forest, which is why so many mythical creatures show up there, but there's evidence that they could live elsewhere as well. Dragons, Hydras, Manticores, Timberwolves, Parasprites, Vampire Bats and Cockatrices have all appeared in the show, and most have been defeated in non violent ways.
Then there's the weird magical artifacts. A magical amulet that granted great power and great insanity was on sale in a strange little shop. A comic book store apparantly sell comics that can literally suck ponies into them so they can live out the story. Poison Joke and Hearts Desire are both plants with unusual magical properties. Love poisons have made an appearance.
I'm fairly new as a GM, so I can't really suggest storylines, but MLP has a lot of stuff that make it an interesting setting. With a bit of creativity, any of the things above could be turned into stories. It might be helpful to know the ages of the players.
I'd reccommend looking at this webcomic
for some more ideas. It's made with screenshots of the show, and works on the premise that instead of being a story for the show, it's a story of a D&D game. It starts out fairly adventure-y, then the players derail the plot spectacurlarly and turns more slice of life.