The 150/160cc commuter segment is a great one to be shopping in for city duties because it is packed with excellent products that are comfortable, decently powerful and quite fuel efficient. Bikes like the Bajaj Pulsar N160, TVS Apache RR 160 4V, Honda Unicorn / SP160 and the Yamaha FZ models would be our top recommendations in this class. 

The 350cc segment - while much larger - is geared to provide a more laidback, leisurely riding experience, and this is why you might think that these bikes "lack pickup." You should ask yourself what sort of riding experience you resonate with first before you start shortlisting vehicles. 

Some bikes in between these two segments that also warrant consideration are the TVS Ronin, Bajaj Pulsar N250, Honda CB300F and the TVS Apache RTR 200 4V.

A test ride of everything you're considering will help you decide. 

In the 150/160cc category, your best bets for a comfortable and fuel-efficient machine would range between the Honda Unicorn / SP160, Bajaj Pulsar N160, TVS Apache RTR 160 4V and Hero Xtreme 160R 4V. 

Depending on your physique, each bike will fit you differently. So, we would recommend a test ride of all bikes on both good and bad roads before you make a purchase. 

If you are open to the idea of a larger, premium machine, then bikes like the TVS Ronin, Royal Enfield Hunter 350 and Honda CB350 will be the options we recommend. If you want to instead go for a commuter bike, there are loads of great options in the 160cc space, such as the Honda Unicorn / SP160, Bajaj Pulsar N160, TVS Apache RTR 160 4V and Suzuki Gixxer. 

Take a test ride of all the bikes you shortlist with a pillion to see what suits you best. 

Considering your height and your back issue, you will require something with good suspension, a low seat and a comfortable seating posture. Very few bikes amalgamate all three, so we have chosen to prioritize suspension over an ultra-low seat. Over time, you can work around that issue and even get comfortable with it. 

Some options in the 150-160cc space to look at are the Honda Unicorn / SP160, TVS Apache RTR 160 4V and the Bajaj Pulsar N160. All have seat heights under 800mm and have compliant suspension setups. 

If you want a larger machine under the 350cc bracket, then you can consider the Royal Enfield Hunter 350 as well as the Royal Enfield Meteor 350. The latter has a lower seat, but its feet-forward seating position won't be very comfortable over bad roads. The Hunter has supple suspension, and while it has a taller seat, its neutral seating position will be better over bumps. 

We would strongly recommend taking a test ride of whatever you decide to go with to make sure you're comfortable with the bike.