I am looking for a compact and safe car with an automatic transmission that can easily navigate ghats. My budget is around ₹10-12 lakh. My family car was a Swift, and its dimensions worked well for my parking spot.

The Citroen C3 Turbo-AT is an excellent crossover hatchback that's compact in dimensions, packs in strong performance, and it'll easily fall within your budget. But go for it, only if there is a Citroen touchpoint near you. 

The Nissan Magnite Turbo-CVT/Renault Kiger Turbo-CVT are also good, value-for-money options. And even though both these are slightly larger than the Swift, they are narrower than other turbo-automatic compact SUVs available at this price. It makes them relatively easier to navigate.