Well there's the LEGO series and because there are so many of them from LEGO Star Wars 2 all the way to LEGO Star Wars: The Force Awakens choose the ones that interest you.
I would have mentioned the Forza series, Project Gotham Racing series, Burnout Revenge, Split/Second, Sonic & Sega All-Stars Racing (got it on the PS3 but the 360 version also has Banjo Kazooie in it), Test Drive Unlimited and some of the Need for Speed series as possible choices. One question that I have to ask, do you like racing games? If you do it is at least much easier to answer since many of the non-violent games from the Xbox consoles are from that genre. I can understand what you mean considering one of the main strengths of the Xbox consoles are its more maturer and violent library even back during the OG days while the Sony and the Nintendo consoles are more family friendly or at least balanced across various demographics. I think they had games from the adorable days of early Namco. I might also suggest some of the arcade games that were brought to XBLA. There's even a what-if scenario with Bardock getting to fight Goku. Might I suggest DBZ Burst Limit? It's like a much better version of Budokai 1, in some ways. Just be warned that one of the tunes in the game is probably one of the most heart-crushing tunes in video games, in my opinion. It does get kind of confusing, but the game has a scene that indirectly acknowledges about how music is considered art, but games are left in the dust. It gets even better with all of the playable characters besides Frederic being named after music terms.
These moments have paintings and text accompanied by music he composed in life. It also doubles as education for kids, as there's cutscenes about Frederic Chopin's actual life. A dream world where musical anachronisms run commonly. It's an RPG about a real-life pianist, on the night of his end. Get the PS3 version, if you want a more complete package. While the story can be very political/philosophical, the violence in Eternal Sonata is more cartoony.