Is there a reason to wear special nice clothing on Hanukkah?
I would guess not as since there is no festive meal, it doesn't seem like it is a festive day.
The Kaf HaChaim http://hebrewbooks.org/pdfpager.aspx?req=14422&st=&pgnum=340 says that there are 3 levels of nicer clothing. The nicest ones are for Yom Tov, the next level is for Shabbos, and the lower level is for Chol HaMoed, Rosh Chodesh, Chanuka & Purim.
Darkei Chaim Veshalom writes that the Michas Elazar would wear his Shabbos clothing and Shtreimel from before he lit Chanuka candles until he went to sleep.
However, Chabad custom is to wear normal(weekday) clothing even when lighting.