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.