Yeah, I'm kind of interested in when that 4 months is in the year. I was there a few years ago February time frame, and it was just getting into the really hot time. Would not want my 4 months to be March, April, May and June - that's for sure.
I was there for business - interesting city, certainly lots to see and do, though like everywhere the traffic can be oppressive. Having a company car with a driver and staying at a stupidly posh hotel (yes, humblebrag) meant I certainly didn't get to experience the real city. But I did get out to Golconda, Chowmahalla and the Qutb Sahi Tombs. The last two are highly recommended and I would love to go back to Qutb Sahi as (three years ago) there was a considerable amount of reconstruction going on. It was amazing as it, but would love to see it when they are done.
I did some solo traveling, self-funded and not posh, after my business trip to Rajasthan (highly recommended). The pollution and poverty is pretty extreme, and when it involves children on the side of the road, it hits me hard. That said, generally the people are absolutely wonderful, and the food is ridiculously out of this world. You think you know that cuisine, but you don't.
Got hustled a lot, and that wore on me eventually. I like to interact and talk to people, and Indians are generally also very friendly. But certainly in Rajasthan, the hustle was to feign interest in you and where you were from and then explain they were an art teacher at a local school, and would you like to come see our exhibit?...
This happened to me multiple times a day, and when you say no things often turned a little ugly as they were really disappointed that you weren't wanting to come in and spend money. Again, I totally understand given the standard of living, and those hustlers were obviously going to get paid a finder's fee if I came in and bought something. It eventually led me to be less open and chatty with people I met, unfortunately.
I've done a fair bit of traveling all over the world in my time, and I found it tough there frankly. Both the poverty and the chaos and congestion can weigh on you a bit. Getting a taxi from the airport is an adventure.
I think it would be amazing to live there as a local/expat for a short amount of time. There's so much to see in that country as well, though the time to travel distances has to be taken into effect as at least driving is a much slower process than you might anticipate given their condition and congestion.