How much are internal flights in the US? We have some ridicously low cost no-thrills airline in the UK that do well for short journeys.

In ask because it very easy to get low cost flights to New York from my local airport, rather than travelling to london to get a competitive price for a flight directly to Chicago. I'd also like to stop off in New York so booking it seperately could make sense rather than the hour or two a connecting flight allows.

So my question: What web sites can I look up low cost no-thrills domestic flights in the US?