Well it stores it internally (its buried in the code). You can check the code by typing edit uiimport. uiimport does not really output the filename selected and I wouldn't recommend changing the code in there before backing up.
An alternative solution might be:
[filename,path] = uigetfile; % opens up a similar dialog to uiimport to select a file
uiimport(fullfile(path,filename)); % directly imports the selected file
doc uigetfile
