I suppose a space elevator is entirely possible (we would need very strong materials, such as carbon nanotubes, to keep such a structure together), but whether or not it is worthwhile is another question altogether. Considering the costs involved, it would probably be both easier and more enviromentally friendly (as in the money could be better spent on other green things) to simply store radioactive waste in underground storage facilities.
One thing that has captured my interest is the idea of green roofs. The idea is essentially to have a "garden" of sorts on the flat tops of buildings. It saves on insulation, absorbs and cleans rainwater so cities don't become flooded as easily, you can grow fruits/vegetables/whatever, less repairs are needed (surprising I know, that's something I'd like to research in more detail), filters CO2 from the air... I could go on. Last but not least, it would look rather cool.
