A full-scale replica is already in the Smithsonian NASM
The Structural Dynamic Test Vehicle, to be exact:
http://collections.nasm.si.edu/code/emuseum.asp?profile=objects&newstyle=single&quicksearch=A19870193000
The museum could always surround this version with some of the real
HST instruments that used to be on the satellite for that extra
authentic space look.
Here is a proposal for a possible use after the main mission of HST:
http://www.coseti.org/hst-jwst.htm
