Yes, the SR80's are excellent home listening headphones, but the open back design does leak the sound.
In-ear headphones do have a different character to the sound than full size on-ear headphones, but can sound equally as good. I'm not sure what budget you have allocated, but below are some ideas:
Ultimate Ears Super.fi 3 Studio - Single driver earphone. Good fit system with over ear loops. Good sound quality. Maybe a little lacking in bass response.
Ultimate Ears Super.fi 5 Pro - Dual driver earphone. Good fit system with over ear loops. Good sound quality with improved bass response over Super.fi 3.
Sleek Audio SA6 - Single wideband driver earphone. Very small design makes it comfortable in the ear. Excellent midrange response. Excellent sound stage, i.e. ability to hear instruments around you outside your head.
Klipsch Image X10 - Single wideband driver earphone (same driver as SA6, but very different character to sound). Very small design makes it comfortable in the ear. Excellent bass response. Excellent sound stage (similar to SA6).
Ultimate Ears Triple.fi 10 Pro - Triple driver earphone. Good fit system with over ear loops. Excellent bass, mid and high treble response. Very well balanced sound.