vintage design magazines  

Are you planning to use them for personal use or are you planning to donate the magazines to an architecture/design related institution/library that allows access to the general public? 
If your set is complete and comprehensive, I had seen in some libraries bound the magazines together like a hardcover book arranged by title and year of publication and available only as reference materials for doing research.  The only challenge I could think of is finding an institution that will be interested in acquiring a big stack of old/older magazines in the digital age.  A design related library will probably keep these on their stacks for a long time instead of a public library that has a tendency to discard older materials to make room for new ones.
If your budget permits this for personal use, this is one of the ways to keep them.  You could also get those inexpensive but sturdy magazine holders or vintage plastic ones (that depends on how big your collection is and if it fits all the format/size of your magazines uniformly).
If your goal is to find an interested party to sell them, try the 'buy & sell' link of this site.  I hope this helps.
Also, please do not cut them up and sell on ebay as vintage ads.

I had a somewhat similar situation when my father died - that is, if you're looking to donate.  I think I gave a set of 90 issues of Design Quarterly, from the Walker Art Center, to Art Center here in Pasadena. I'll check my notes to be sure, if you like. Right now, I'm trying to find someone to take a catalog (pamphlet, really) of an Akron Art Insitute design show - Akron (now) Art Museum will take it, but without any real interest.
Whatever you do, check with the librarian first. My father donated a bunch of books to Parsons, where he taught, and later discovered that they weren't added to the collection, just left out for students to take if they wanted, which wasn't what he had in mind. 

That is an icredibly impressive list of publications.  If you intend to access these just for personal viewing, I would break them down as follows:
Interior Design/Furniture realated: Interiors, Canadian Interiors, Md, Abitare.Shoner Wohnen
Architecture: Arch Forum, Arch Record, Arch Review, RACI, Canadian Architect, RAIC journals, Progressive Architecture
Industrial Design: Industrial Design, ID, Design Brick and Tile (maybe)
Fine Art: Arts Canada and Canadian Art
Sounds like an amazing collection!  I encourage you to post them on the Radar if you are interested in selling the collection.  I know I would be interested.

thanks for your input and suggestions.  I have been working with my father to try to encourage him to donate the magazines to an interested entity that would make them available for research purposes.
 The university here did take his papers and models and wrote and published a beautiful book on his work.
I think you hit the nail on the head in that there is some 20 plus boxes of magazines.  If I had the space I would keep them myself and offer them on loan for informational purposes but finding someone who wants to curate and manage this much paper in this digital age is indeed a tall order.  
My dad is a particular fellow and the magazines are in perfect condition but as they are moved about and stored damage will inevitably happen.  I hope that by having them slowly transported to me to review will be the first step towards finding a safe place for them.  I have been in touch with the dean of environmental design  etc. and the author of the book as well as the other educational institutions he taught at over the years but right now am meeting resistance from my father who fears the same kind of outcome as your fathers books Kate.
jesgord, thank you so much for helping me break things down a little...I appreciate your input