Car travel tips are tricky...I'd suggest you avoid driving altogether!
Do Not, I Repeat, Do Not, Drive Yourself
Do not consider driving while you are there. It’s a really bad idea. India is like the most difficult driving experience you could imagine, times 100. If you were to have an accident here, you may well be mobbed and beaten (I saw it happen on my last visit to Calcutta—it was my husband’s first day in India and it was a bit of an eye-opener for him to see a taxi driver, who’d hit a beggar, dragged from his car and beaten!). If you damage anyone or any property, you would also face hideous legal issues. It’s soooo not worth the risk and best left to an expert local.
Actually out of around ten trips I have personally witnessed two people get run over by cars. The other one was a pedestrian who stepped off a roundabout carelessly and got run down. So be careful!
Hire a Car with Driver Instead
You can hire a car with a driver quite reasonably for a half day or a full day (exact prices depend on the city). This is for those times when you want more than a quick trip somewhere in a taxi. Oh, you can also negotiate a taxi driver to be an impromptu tour guide for you. My friend Kara and I did this in Bombay and it worked out really well. It would really depend on the driver though, and how well he spoke your language. If it’s Summer or Monsoon, don’t forget to ask for a car with air-conditioning, because it’s not standard.
Other than that, autorickshaws work well for around the city, or rickshaws if you're not going far but just can't face walking any further.