Since you are a first-time car buyer and will go off-road occasionally, it makes sense to go for an SUV or a crossover, which has the double benefit of a high seating position. 

It also gives confidence to first-time buyers behind the wheel and a high ground clearance to tackle bad roads and speed breakers. You could consider the Maruti Suzuki Fronx 1.2 AMT, which has a spacious and comfortable cabin, is well equipped, rides well both on and off road and has key safety features
 

The Maruti Suzuki Fronx is based on the Baleno, and mechanically and structurally, both are very similar. 

Thus, both will be very similar when it comes to safety, too. As for the crash safety rating, yes, the Fronx has secured a 4-star rating in the Japan NCAP crash tests; however, the Baleno has secured a 5-star rating in the BNCAP tests. 

So the Baleno is safe too, if not safer, you must bear in mind that there could be differences in the export model. As for the engines, both Fronx and Baleno use the same 1.2 liter naturally aspirated unit. However, the Fronx also comes with the choice of a more peppy and lively 1.0 liter turbo petrol engine

We suggest going for the Maruti Suzuki Fronx. It has SUV styling, higher ground clearance, and is a more modern offering than the Maruti Suzuki Baleno. Since Maruti is expected to update the Baleno in the coming months, buying one now may leave you with a car that feels dated soon. SUVs also tend to enjoy better resale value in the Indian market, which works in your favour if you plan to upgrade later.

Our preferred engine choice is the 1.0-litre turbo, but if your usage is mostly within the city and you’re working within a budget, the 1.2-litre naturally aspirated engine will serve you well too.
 

Given your limited running, a hybrid or an EV will not make the most financial sense. 

We’d suggest you consider a petrol-automatic. There are many options in your budget, though the Maruti Suzuki Brezza, Maruti Suzuki Fronx Turbo and Toyota Urban Cruiser Taisor Turbo are the ones that will best meet your requirements of good economy, low maintenance and reliability.

The Brezza is an upright compact SUV and has the roomiest interior of the options. Its 1.5-litre engine, however, is pleasant but unexciting.

The Fronx and Taisor are essentially the same car. Both are best with the turbo-petrol engine and automatic gearbox option. Performance is impressive, and fuel economy is also good.

Both cars offer comfortable seats and a comfortable ride, well-tuned for Indian roads and city usage, making them ideal for daily commuting. Maruti has already proven its hassle-free ownership experience to you, while Toyota is also known for reliability and smooth ownership.

Between the two, you can pick based on which design, brand and feature mix you prefer, but either will tick your key boxes of comfort, mileage and peace of mind.
 

That is quite a tall order to fit into your budget of Rs 10-11 lakh. However, given your requirements, we would recommend the Nissan Magnite or the Maruti Suzuki Fronx. 

Both compact SUVs give the option of a fuel-efficient naturally aspirated petrol engine with an AMT auto gearbox at a good price, or a more powerful turbo-petrol engine with an auto gearbox that's not as fuel-efficient, but much smoother. 

Both have robust suspension that should be capable both in the city as well as on the highway. That said, while both can fit 5, the back seat will be a tight squeeze for 3, but at this budget, almost every car would be. 

Here, the Nissan Magnite has the edge on space, and overall, it is more affordable and a better value, too. Hence, it would be our pick for you.

As you've mentioned, the Hyundai Exter is the smoother and more refined car of the two, thanks to its four-cylinder petrol engine. 

Its transmission is also relatively more seamless, and overall, Hyundai cars have a better reputation for their sales and support network too. 

Other options you could shortlist are the Maruti Fronx or Toyota Urban Cruiser Taisor 1.2 petrol AMT.