Is early to mid-November a good time to do a trek of the Himalayas? Are there treks even available at this time, or is this the off season?

I'll be in Delhi, Jaipur, Agra (and possibly Varanasi) from Nov 4- Nov 15. During this time, I would like to squeeze in maybe a 2-4 day trek of the Himalayas in Himanchal Pradesh or Nepal.
I have never done a trek, so I am a beginner, but I am in decent shape.
What company do you recommend I use to set this up?

Also, which Himalayan area is better for beginner trekking, Himanchal Pradesh, or Nepal?

I am not looking for anything too serious. I just want to do an easy to moderate hike of short duration, so I can view some of the Himalayan peaks from a distance. I'm not actually looking to scale these mountains!