Snow Globes... Any reason to keep them? Is there anywhere or way to display them? Or should I sell them back?

Also, in my Lucky 38 suite, there is a snow globe on a shelf above what looks like a bobble-head display. I can not seem to touch it, with either the "E" (place in inventory) key or "Z" (drag item about) key. Am I being a cat with an unreachable ball of string here?

There is an NPC in the Lucky 38 who likes collecting them and will tell you this. Another NPC will take them from you in exchange for caps. They will then appear on the stand in the Presidential Suite. There are seven in the base game, plus one in each DLC.

actually told me about them, and it looks like she will buy them, too. Is this not correct? Or did I skip talking to someone?

She's the one. BTW the snowglobes you find in the DLCs automatically go to the display area, and you get paid, as soon as you find them. From your description it sounds like you found one of the DLC snowglobes already, and it is in place on the shelf.

Yes, that display is where they'll end up after you sell them to Jane.