As between them, the Cypress doesn't come with fenders/basket, but those could be added if she wanted them. It looks like 24 speed, so 3 chain rings on the front and 8 gears on the cassette on the back. It will be a little less of a cruiser and more of a fitness bike. It would be better equipped to deal with any hills.
It looks like the Simple comes in a single speed (no gears) or 3 or 7 speed. Even if it's relatively flat, she may want some gears. It will ride a little more like a beach cruiser.
It depends on what she wants and feels comfortable on.
Hey there! I haven't shopped for that kind of bike for a while, and when I did, I bought used like you did and spent about $200. But Giant brand bikes are good quality in general, so for a new bike that doesn't seem crazy high. I'm looking at road bikes right now and one of my top contenders is a Giant.
Giant bikes are very good. They are one of the big brands and manufacture bikes for other major brands (Giant owns the factory in Taiwan.) I have two high end Giants that I really like. They offer a good value for the $$. As far as pricing for "Lifestyle Bikes," $375-500 is the typical price range. Most shops will offer a 10-15% discount on accessories like the basket if purchased at the same time as the bike.
Your mom does NOT want a single speed even if she's just going to ride the Beltline. There are too many hills to get to the Beltine.
Alas, there aren't any bike shops in Atlanta that deal exclusively in really good used bikes. SOPO Bikes and Beltline Bicycles occasionally have fairly old but reconditioned bikes for sale. You might want to call to see what they have. I'm not sure if it would be worth the drive for you. Roswell Bicycles *may* have some used bikes as does Cannon Cyclery, but their stock varies day to day.