Photo 01
The font used for the first business, it looks to be a serif font. which is seems to be a better choice for a Jewelry store, however I think that the elegance of typeface is lost in round and thickness of the letters. I would suggest using more of a modern or transitional Serif with more sharpness within the lines. It would display more of a cleaner look for the type of business.
Photo 02
The octagon shape behind the name makes me thing that it the business might be in Tech or Mechanics. However the choice of font makes me think that the business is food related, like a diner or Cafe.
The jewelry store sign is indeed in a serif face but I agree it is not at all elegant.
Good thought about the tech or mechanics in Photo 02 (due to the shape). In class I’ll “reveal” the business.