Of course different people like different things - thankfully.
It's disappointing you think it's become less safe, particularly given that you're in a good position to judge. Presumably that's the centre of Brighton though, not the whole city? Stoneham Park is quite nice isn't it?
Cool. I don't live or know those areas, but plenty will. It might be difficult on the budget, but it would be nice if you find somewhere with potential to extend (up or out) in the future.
So what exactly do you want?
What do you want from the location - remote, family area outside of town, near the sea, near the city?
What do you want from the property - bungalow or semi out of town, garden flat nearer the centre?