The Shulhan Aruch, in Siman 301, rules that one may wear his Talit in the public domain without an Eruv, provided that it is wrapped, at least, below his shoulders. If he wears it only around his neck, it is prohibited, since this is not the normal way to wear a Talit. One may, however, wear a scarf around his neck, since that is the usual way.
Hacham Ben Sion says a Hidush that if one is coming out the Mikveh and wants to take his towel with him, he may wear it draped around his shoulders. He also says that one may take his arms out of the sleeves of a jacket and wear it draped over his shoulders on a hot day, as that is also the normal way.
SUMMARY
One may wear a Talit, a towel or a jacket draped over his shoulders, or scarf around his neck in a public domain without an Eruv.
Daily Halacha
Carrying on Shabbat: Talit, Scarves, Towels and Jackets
Lectured by Rabbi Eli Mansour