You probably know you can't reserve at Many Glacier, and last year the second week of July it was hard to find a site even at 8 or 9 am.
Rising Sun CG, according to park stats, doesn't usually fill up till afternoons, but best get a site as early as you can to be safe. They have fire rings/potable water/bathrooms $20.00/night. $10/night for us old folks with a "card"
I don't always trust those times they post...they say about Many Glacier too that it fills by noon or something but in my experience it is very difficult to find a site after 9 am and people last summer were looking for sites at 7 am.
St. Mary might be your best choice...and don't forget the St. mary KOA too, if you get desperate.