1. I have done a lot of searching for you, but have been unable to find a definitive answer, which I regret.
2. The Sir Walter may have been one of a chain of hotels that began in or around Jacksonville, Florida. I have found these references to the Robert Meyer hotel chain there, some with postcard views. Note that they are all several decades old.
a) The Roosevelt, a Robert Meyer Hotel in Jacksonville, Fla. http://jpl.coj.net/html/dlc/florida/pc/0...
b) Hotel Robert Meyer Hotel also in Jacksonville, Fla. http://www.cardcow.com/13719/hotel-rober... http://jpl.coj.net/DLC/Florida/pc/PCJPG/...
c) Hotel Windsor, a Robert Meyer Hotel, again in Jacksonville, Fla.
d) Emerson Hotel, location unknown
3. This may be a complete red herring, but there used to be a hotel called the Sir Walter Hotel in North Carolina. It was built in 1923, as a hotel and convention centre. In the 1970s it was converted into apartments for senior citizens. None of the following webpages has any reference to Robert Meyer, which is an obvious negative. The different location also suggests a wild goose chase. However I can't find references to any other hotel simply called the Sir Walter.
a) This website, about the hotel itself, refers to it as the Sir Walter Raleigh Hotel - it was located in Raleigh (do you see the humour?). Also notice the remarkable similarities between views of this hotel and that of The Roosevelt.
b) However, this other webpage, on actions of the civil rights movement, in Raleigh, refers to it as the Sir Walter Hotel.
c) Here is some more information about Sir Walter Apartments - the building is on the National Register of Historic Places.
d) Finally this article, again using simply the Sir Walter name, mentions the possible restoration of the building as a hotel. http://www.bizjournals.com/triangle/stories/2002/04/08/story1.html?page=1
4. I have tried to find out who this Robert Meyer was.
a) I have found reference to to a hotel chain proprietor, by the name of Robert R. Meyer.
(i) This Robert Meyer's holdings included the Hermitage Hotel in Nashville.
(ii) However the concise history available on the hotel's own website has no reference to the original owner.
b) My instincts tell me that there is a website somewhere with the definitive answer. Good luck in finding it!