For small rust spots try
Brownell's Oxpho-Blue. It's the best cold blue I've tried (the Oxpho-Blue liquid, not the cream or paste based stuff). Mostly for firearms but works on any carbon steel to remove and neutralize light surface rust. I'd usually wind some fine steel wool around cotton swabs, dipped in Oxpho-Blue, and lightly rub the rust spots to remove the excess while simultaneously blackening the bare steel to prevent further rusting.
I wouldn't treat an entire frame with the stuff, but to minimize rust on a bike that I just wanted to knock the dirt off of and protect against further rusting, it should do fine.