Binghamton is a city in the eastern most extent of the Southern Tier of New York and the lower right-hand corner of the Western Tier of New York. At the crossroads of the Southern Tier Expressway (NY Route 17) and Interstates 81 and 88, it serves as one of the principal gateways to western New York. The city competes with upstate New York cities - Rochester, Buffalo, Syracuse and ? Albany? - for the The Golden Snowball Award.
It is very easy to get from Rochester to Binghamton. Get on I-390 and head south. When that road ends, go east on I-86/NY 17, and, sooner or later, you'll get there. As for what to do when you get there: See the Binghamton Mets (baseball) or Binghamton Senators (hockey) play Try a Spiedie In August go to the SpiedieFest and Balloon Rally Binghamton now has a city wiki as well, found at www.BingWiki.org.
The wiki is on RocWiki's interwiki map and can be linked to directly as BingWiki. See their Rochester page or link to it using: [wiki:BingWiki:Rochester,_NY Rochester]