Is there a reason you don't want bees? They are awesome for your garden... anything with flowers will attract bees and I only like flowering/fruiting plants so take that in mind with my suggestions. Also, consider how tall you want the trees to be and that will help you weed out your choices.
For privacy along one of our fences (in Melb near you so they would suit your area) I chose callistemons as they are fast growing, native and have lovely flowers, a loquat as they fruit and have gorgeous big leaves and a feijoa as they are nice and dense for privacy and fruit, but they are slow growing so I put it at the edge where I'm not fussed about privacy as quickly.
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