Tyres that could go off-road? Sorry, no recommendations on that front because not many tyre makers are that adventurous. But for other needs I think Apollo Aplha H1 should be good. Tyredekho team hasn't tested these, as they are fairly new to the market. But we have heard good reviews from the team zigwheels.
They tested these on Duke 390. Read the review here. Hope this would help.