I spent a few months travelling around India last year and had the same issue.
In any of the cities you mentioned, in my opinion, you really don't want to be running on the streets. There's chaos at every junction, pot holes, stuff in the way. I mean, you could, but it'd be a very interrupted run and not very enjoyable. If you're in the villages, it's fine of course - and great fun - but not the cities.
However, whenever I arrived in a city, I'd usually just Google city + running. There was nearly always one or two common places people go to run. Thankfully, lots of people have asked these questions before! There are almost always gardens/parks or things like horse racing tracks that are open to the public. Grab a tuk-tuk for a few rupees and you're there. It's not ideal, but it's your best bet in India I think.
In Jaipur, for example, there's Central Park. This is a great place to run and has a looping path that's about 5k as I recall.
Best of luck - have fun!