I understand that one says Birkat Ha'Ilanot on seeing the blossoms on a fruit tree. Does a tree that blooms but doesn't produce fruit get a bracha? And if so, which one?
I'm afraid the bracha you are referring to is only on the blossoms that lead to fruit on the fruit trees. See Mishna Berura OC 226 sk 2
There is another bracha on nice 'creations' (including trees) but it generally accepted that it is only recited on the most beautiful creation you have ever seen till now. Since we can not measure 'beauty' very well, we generally avoid saying this blessing. See Shulchan Aruch OC 225:10 and Mishna Berura there. [I note that this is AFAIK the very widespread custom; however, it might not be so well based in the sources. See Shaar HaTziyun sk 34 for details.]