Clean them right after cooking or at least leave them soaking in water. Stainless is fairly easy to clean until the food cakes itself on. It also helps to heat the also heat the pans with a little bit of water over the stove, not to boiling temp, just warm, before scrubbing with a stiff brush. Anything that doesn't come off can be hit with some steel wool and it'll work like a charm
Speaking of copper cookware, I need to have some re tinned, does anybody have a recommendation for a good whitesmith in capital?