If you haven't gotten an answer from another source yet, Coca cola used signs with those stars in the 1960's. As far as what its worth...as much as someone is willing to pay really. Most of the time I see menu boards around $150 with maybe one crack in it but they are also a little older. If its clean of yellowing and no cracks even minor ones I could see you getting $200 for it. Of course different areas prices can vary. I'm not an expert.
1960s as mentioned above, but the frame doesn't look original. If the condition is excellent (no cracks in the plastic), the original frame is present and it lights up, then value would be $3-400 IMO. Here's a link to one that sold at auction in 2020 with a hammer price of $350:
https://www.liveauctioneers.com/item/90604366_1960-s-coca-cola-light-up-menu-board
