October to March is the best time to visit Delhi, with February and March arguably the sweet spot.
October offers warm, dry, pleasant weather as the monsoon retreats, and coincides with Durga Puja, Dussehra and often Diwali — the city at its most festive. The trade-off is that air quality begins to deteriorate towards the end of the month.
November to January is peak tourist season and the temperatures are ideal for sightseeing, but this is also when Delhi's air is at its worst and when fog disrupts travel most. Many visitors still choose this window and manage fine, but it is worth going in aware.
February and March combine mild temperatures, improving air quality and blooming gardens, with fewer of the winter's disruptions. Holi usually falls in March. For many travellers this is the best compromise.
Avoid April to June. The heat is extreme and genuinely limits what you can do.
July to September is workable if you don't mind rain and humidity. Prices are lower, crowds thinner, and the monuments look their best against green surroundings. Waterlogging is the main practical problem.
A note on festivals. Diwali (October or November) is spectacular but comes with the worst air quality of the year and heavy crowds. Holi (March) is enormous fun but be prepared to get thoroughly covered in colour, and note that many businesses close.