St Augustin is not that far from the terminal, but there is a shuttle bus that goes to Nice Ville station (only takes 15 minutes unless the traffic is bad), and you have a lot more choice of trains no matter where you're going.
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There's indeed a railway station close to NCE as JGPH1A pointed out. Only local trains stop there.
Otherwise to go to Nice Ville station you have the choice between bus line 99 "Direct gare", 4€, or bus 23 (take it at T1), 1,30€ (but it takes much longer than bus 99).