I went to the Jilted Anchovy as recommended in the Clovelly suburb profile and have to admit the pizza was pretty good.
The thing I've noticed about pizza prices in Sydney's east - is they are not cheap. Some pizzas are crap and they still charge you a lot for it. But other places like the Jilted Anchovy charge approx $11 for a small pizza but at least they are good.
There are a couple of pizza places in Randwick. I haven't tried Arthurs, but the other place I went to, which is a restaurant and pizzeria, had what I reckon was one of the worst pizzas I have ever eaten. It felt like a brick in my gut after I had eaten it.