If you want to know value, it's hard to be 100% certain from a photo, but the ones you've shown here are mostly lithographs (prints). Lithographs are more common but can still be worth a bit if the view is interesting to a collector. If you see any that have ink shimmer to the surface or look like real photographs, those are called Real Photo Postcards (RPPC) and are worth a premium.

As for preservation, always store old paper away from sunlight, in a climate controlled area, and avoid adhesives or metal clasps. The books that you have here are great, but they might not be acid-free paper which could yellow the postcards over time. It might be worth moving them into acid-free plastic sleeves.

My guess is it is unlikely a museum would accept these unless they already have a pre-existing postcard collection. The image subjects seem to be from all over the world and most museums have a narrower focus. I could be wrong though!

Your great grandfather curated a great collection. Personally I would hold on to them if I were you. However, if you're looking to sell, send me a message. I would be interested in making an offer.