Are you asking about Jefferson/Adams/Washington or the earlier Pilgrims?
The first settlers had some fairly narrow ideas about what was permissable/godly. A good way to imagine their hymnody is to think of "My country 'tis of Thee" sung plain, with no instrumental backup. Instruments tend to play with a good beat, beats make people boogie with their bodies, bodies are hotbeds of sin and vice, so no go.
The constitution crowd would have heard a much broader range: meatier church hymns, accompanied by organs in wealthier communities; tavern ballads, instrumental pieces played by accomplished daughters in parlors, minuets and contredanses at the balls.
The music to our ears would sound fairly mannered and upright -- but still zesty! -- with flute, violin, and cello predominant, after the human voice.
They would have heard plenty of music, but a much smaller percentage of it would've been at concerts. People made their own music then, as in most of human history; it's only our current society that's trained us to think we need to leave it to the experts.