Suggestions on long Layovers in Delhi (DEL) or Mumbai (BOM)?

Hello! In late August / September I’m looking at flights from the US to India, with layovers either at DEL or BOM ranging from 8 to 15 hours with morning or into late evening as choices, to another Indian city. I am going solo on a work trip but would like to get as much bang for the buck for sightseeing and exploring. Assuming I am awake and not needing to sleep, any suggestions for short/medium layovers? I am 43M and will be visiting for the 1st time ever, and am both excited but nervous.

I like trying different foods and seeing some historical sites, can handle a good amount of walking/hiking, but don’t want to push my luck by getting back to the airport too late. Any good experiences with layover visits to either city areas? Thanks for your advice.

Suggestions on long Layovers in Delhi (DEL) or Mumbai (BOM)?