Is it smart to rent a car for travelling from Phuket Town > Rawai > Patong as a tourist?

As a first timer to Phuket, one of my plans would be to travel from Phuket town > Wat chalong > buddha > rawai sunset > dinner > sleep a night in rawai > patong the next day. This would mean I need a car rental. Is it feasible/smart to rent a car in Phuket for this? Or is driving a headache in Phuket? As the above itineary seem infeasible with taxi, right? The major concern with taxi is unable to travel to Rawai without a car. As well I’ve searched online it seems car rental for two days is around 2600 baht (excl gas). How’s this compared to taxi fare?

I’ve also considered motorcycle but my companion isn’t comfortable riding. I have all my Intl Drivers License and have driven overseas many time. But I’ve also heard stories of traffic jams in Phuket. Thanks for any input!

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