If she likes more of a modern look, I agree, gray, chambray, black, and navy are all good choices. Black and navy will make the colors pop, especially if you use vibrant jewel tones. If she wants pastels, I'd recommend going with gray or chambray.
I did a search on Pinterest for "gray background quilts", hopefully you'll be able to see the results here:
https://www.pinterest.com/search/pin...yped&term_meta[]=gray|typed&term_meta[]=background|typed&term_meta[]=quilts|typed
Your daughter might change her mind about the gray once she sees some lovely examples.