Since you haven't specified what style of bike you want, nor given some details about your physique, recommending something concrete will not be possible. However, we'll give you a variety of options to choose from, spanning multiple classes. 

In the neo-retro space, you can look at bikes like the Royal Enfield Classic / Bullet / Hunter 350, TVS Ronin, Triumph Speed T4 and Honda CB350 models. These will have a relaxed riding experience and a plush, comfortable ride quality. The Speed T4 will be the quickest and most responsive of them all, but still very manageable for daily use.

If you want something sportier, the KTM 250 Duke makes for a compelling option for your one-bike garage. 

If you're leaning towards the more adventurous side of things, then the Hero Xpulse 210 and the TVS Apache RTX 300 are the way to go. 

It would be advisable to take test rides of all of these bikes to see what style you prefer and which bike you are most comfortable with. 

Within your budget, you should look at bikes like the TVS Ronin, Royal Enfield Hunter 350, Honda CB350 and Triumph Speed 400. Of these four, the Speed 400 will be the fastest, but it also offers a good level of comfort and usability for daily use. Its tractable engine, short gearing and light clutch will make it a good city companion. 

The other three bikes are more relaxed in their nature but will still offer a tangible step up from your old Hornet 160, especially in the comfort they offer you. 

Take a test ride of these bikes to see which one suits your riding style best before making a decision. 

Since you've said you want something manageable in the city and also stand out from the sea of commuters, we'd recommend taking a look at the Honda CB350 and the Triumph Speed T4. 

Both have upright ergonomics, good ride comfort and have a well-balanced chassis which ticks all the boxes you're looking for. Of the two, the Speed T4 will offer more performance than the Honda, and both are similarly fuel efficient. 

Also, Bajaj will be downsizing all the Triumph 400s to 350cc to take advantage of the new GST 2.0 regime, and these bikes should be released by the first half of the year. Once this move is complete, expect prices across the board to be quite a bit lower, and if you are shopping in this space, it would be prudent to wait a few more months. 

In the 350cc space, bikes like the Royal Enfield Hunter / Classic / Bullet 350 and Honda CB350 trio make for good options considering your mixed usage. All of them have upright ergonomics, comfortable suspension setups and decent fuel economy. 

If you are open to waiting for a few months, Bajaj will be releasing 350cc versions of all the Triumph 400cc bikes. These will offer you noticeably more performance than the aforementioned air-cooled 350s while being priced similarly. 

Both bikes that you have shortlisted will be excellent companions for your long daily run. Both the Honda CB350 and Royal Enfield Hunter 350 have smooth, torquey engines, upright seating ergonomics and a plush suspension setup. If you are a taller person, you may feel a little more comfortable on the CB350 because it is a larger machine than the Hunter, although the RE isn't exactly cramped. 

In a similar price range, you should also take a look at the Hero Xpulse 210. With its long-travel suspension, peppy engine and commanding ergonomics, this could possibly be the most comfortable bike to tackle long distances every day. Its seat height - at 830mm - is on the taller side, but if that's not a dealbreaker, we'd strongly recommend taking a look at it. 

A test ride of these three will help you decide which is the best option for you. 

Between the Royal Enfield Classic 350 and Meteor 350, the former would be our recommendation. The Meteor's feet forward position will transmit more jolts to your back over bad patches of road. Therefore, it won't be comfortable over long stints in the saddle. The Classic's upright and neutral rider's triangle will be easier to live with on a day-to-day basis. 

You should also take a good look at the Honda CB350 models because they have a similar riding experience to the RE 350s. But are much lighter and come with alloy wheels and tubeless tyres. They also have a slip/assist clutch, resulting in little effort when operating the clutch. 

Since you are a taller person, looking at an ADV like the Hero Xpulse 210 and TVS Apache RTX 300 is also a good idea. Of the two, the RTX is the better all-rounder, but the Xpulse is lighter.

Take a test ride of these bikes so you can decide which is a better fit for you.