The AGB star Mira (omicron Ceti) is very likely to be closer to Earth than alpha Herculis. It is probably the nearest to Earth. Here is a paper describing a catalog of AGB stars from IRAS

http://adsabs.harvard.edu/abs/2009JKAS...42...81S

The catalog itself is available at

http://web.chungbuk.ac.kr/~kwsuh/agb.htm

You will have to cross-reference the IRAS numbers with SIMBAD

http://simbad.u-strasbg.fr/simbad/

to determine whether Mira is indeed the nearest.