Since the areas are so close together you should look at all options. What is "best" is extremely subjective and you and your family are the only votes that should ultimately count on that decision.
Compared to Santa Barbara, every city in Blaine County will seem small and quaint, but that is a lot of the appeal. When you are looking for at least an acre, the actual "city" may not really matter as much.
I think you would be doing yourself an injustice if you ruled out either city before visiting them and looking at the available homes.
Because of the limited inventory of homes in your price range and meeting your criteria in Blaine County, I have attached a link that might help you as you do your research before choosing on moving. I hope it helps!
I have lived in that area most of my life and both towns are beautiful and offer many amenities. The best fit really depends on what hobbies or amenities you are desiring to have close by. Ketchum is deeper into the Mountains and is a little more secluded. Ketchum has a nice hospital as well as many unique stores and shops. Hailey has Mountain ranges on both sides and is closer to larger shopping areas. It also has larger grocery stores and food chains. Hailey does also offer unique dining and shops. The two towns are only separated by a few miles.
I would be happy to send you some links to different properties, if you would like to experience what is available. It is a beautiful area - I hope you find exactly what you are looking for!
Have a Great Day!