I really don't know anything about the public transportation. Although South Brunswick is pretty much the same area as Dayton. They share the same school district. I believe Dayton is just a small town within South Brunswick.
I did a quick search on craigslist for South Brunswick and came up with a couple results.
central NJ craigslist > sublets & temporary: search for "south brunswick"
You can also try searching in Monmouth Junction which is also right next to Dayton. I'm sure more people will respond with some other ideas that know NJ a lot better than I do. Good luck.