Independent wrote a list on the "10 best vegan cheeses", including vegan alternatives to mozzarella, blue cheese, cheddar cheese etc.
Personally, I've never been a fan of cheese (vegan or not). I really dislike the taste and even more the consistency so I can't help you choose a good cheese alternative, but as you might already know, there are probably more vegans loving cheese than vegans not loving it so it's a huge market.
Do you have a favorite vegan cheese?