Among the RE 350s, you can consider the Hunter / Bullet / Classic models for their comfortable ride, neutral ergonomics and smooth as well as characterful engine. In a similar vein, the Honda CB350s also warrant strong consideration for similar reasons. 

All the Harley-Davidson X440 models have a similar riding experience and only differ in terms of features and design, so pick the one you like the most. 

Lastly, we would also recommend you take a look at the Triumph Speed T4 and Triumph Speed 400 as they offer great performance and quality at a reasonable price. 

Take a test ride of all the bikes you shortlist before you decide. 

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.