The other weekend - you could do the standard desert tour - rajasthan (jaipur / udaipur etc) .. but going there in the rainy season, and/or the fag end of summer doesnt make sense at all
You could try SIN / DXB / BKK / KUL of course - or also try KTM. Early evening wont make too much of a difference given the time zone it's already night time in anywhere like SIN/KUL/BKK you fly to, if you catch a midmorning flight and arrive there late evening their time. So catch a flight that's like 10 PM or so, arrive early in the morning in SIN, fly back for a late evening or mid morning arrival in DEL. Poke around kayak.co.in or ixigo.com for cheap fares del - somewhere else - del.