There's at least two great options, both downtown: Comics for Collectors on Aurora Street and Providence Hobbies on State Street. Both stores are independent and locally owned, and we encourage patronage of both! There are other locations in town where you may also find games, but their selection is more limited.
Comics for Collectors
207 North Aurora Street (next to Collegetown Bagels)
(607) 272-3007
http://www.comicsforcollectors.com
Hours:
Comics for Collectors (or "C for C") specializes in comic books, but also carries collectible card and miniature games, role playing games, and a limited selection of tabletop games. They will do special orders, and club membership gets you 10% off games. They also have online ordering available.
Providence Hobbies
631 West Buffalo Street (across from Greenstar)
(607) 273-4251
http://www.providencehobbies.com
Hours:
Providence Hobbies specializes in hobbies and games, and carries a variety of tabletop/board games, collectible card and miniature games, role playing games, miniature games, and traditional games. They will do special orders if they don't have the item in stock. Gaming space is available in the back of the store at the new location. They run Magic: The Gathering tournaments on Sundays at 1 pm.
Barnes and Noble, between Tops and Wegmans, also carries some games. These are mostly of the book variety, although you'll find the occasional board game as well.