While I agree that donating to a university or college might be a good way to go, I have to kindly disagree with donating these particular garments directly to a college theater department. The garments would be damaged over time, or at the least significantly altered from fittings, alterations and cleaning, general wear and tear, body soiling and staining, etc. I would think they should be cared for in a private personal collection, a small museum (university or otherwise) or worn by just 1 person who would care for them and strive to keep them original and as pristine as possible.
If the 1 garment you show is indicative of the other garments from your relative, you have some lovely higher end and possibly custom fitted garments of good fabrics and hand detailing. If the dresses are a good wearable size, you might think about selling them on Ebay or similar, or finding an online vintage collectors site where you could place an ad and sell them as a "lot". Not sure if this would be workable, as the postage could be too high to make this profitable for the buyer.