Both sound good. Balmain Lodge is in Rozelle which is a great suburb. It's walking distance from Balmain. You can walk into the city from there too but it will take about 45mins via the Anzac Bridge.
And the Randwick one looks good too. If you like hanging out at beaches, then Randwick would be the go.
But if you prefer a cafe scene and community feel then I'd go for the Balmain Lodge option.