I'm not a big fan of rum, any suggestions for a good substitute?

Bourbon could be good. I guess it would be a concord grape mint julep, not a smash. I also agree with hardlikearmour, gin would be wonderful.

I think it would be really good with a botanical gin like Aviation.

It's hard to reproduce the caramelly sweetness of a proper rum. I much prefer dark rum to white rum for precisely this reason. If you're wanting booze without the rum flavor, your best option is a neutral spirit like vodka, which would be similarly clear in colour with a comparable alcohol content. If you did this, I'd suggest making your sugar syrup with some brown sugar in order to impart a bit of molasses flavor to the drink.