Will Microsoft Word 2011 for Mac only let me type in Times New Roman

You can record a macro to get around the problem. You need the macro to do the following:[space] [left-arrow] Alt-X [right-arrow]

To use it, type 2300 immediately followed by the key you've assigned to the macro. The macro inserts a space character (which will be of the orginal font), goes back to your number, does the Alt-X to convert it to unicode, then goes back to after the space (which is again in your original font). If you don't want to insert a space (if you want the next character to be immediately after the unicode character), add a [backspace] at the end of your macro.

This problem might no longer be bothering you, but I have struggled with this for quite a while. I solved it by deleting the templates normal.dotx which on its own had no effect. Only after deleting the templates AND changing office's default spellcheck language as described here, Word finally stopped to fallback on Times New Roman.