Thank you for your help.  It's normally weeds that volunteer and do great in my yard--so this is a wonderful surprise.  Not only are they not weeds, but they're beautiful native flowers.  

What threw me off re: the Brown-eyed Susan ID is that its leaves are shown on sites to have three lobes (triloba) with finer teeth.  Many of the leaves here appear to have five lobes (two extra lobes off the center lobe) and larger teeth.  What I'm calling extra lobes here may not be regarded as lobes, but whatever they are--I don't see them in photos online.  So either the 5-lobe larger-tooth leaf photos don't make it onto the internet much (maybe b/c once it flowers, the leaves further up the stems that get photographed are 3-lobed with finer teeth)--and/or there's a bit of variation within this one species.  Now I'll be checking out the lobe/tooth situation every time I see a Brown-eyed Susan growing somewhere.  

In any event, it's great to know what it is.  Thanks again.