OK, you haven't mentioned potential dates, and of course we're pretty close to getting into the premium/high season scenario. Thanyapura is essentially in the centre of the island, and to the east whilst pleasant, there's no beaches. On the west, Nai Thon is closest, with the advantage of being near the airport also (south). Decent beach, though swimming in the sea any time west coast Phuket up until December/January is to be avoided (rips/drownings). A few local style restaurants in Nai Thon, though pretty much local fayre, lacking international menus. Not sure if there's a 7/11 or Family Mart, but there will be some near the airport.
Other thing to be aware of, Nai Thon is pretty much Moscow by the Sea, very popular with Russians, which doesn't give me a problem but then again I don't go there. Looking at Google Maps, there are a few options, but you would need to do more research.
That north western part of Phuket is very much the high end of the accommodation market, from Bang Tao/Laguna through to MaiKhao.
If you want a quiet place, with some real local seafood places, albeit with no beach, this might suit:
https://laemsairesort-bke.zoombookdi...e-pay&adType=0
Basic, but good location. Very quiet in scenic area, one of my coffee stops whilst cycling. Some international restaurts in the Pa Klok area, but you'd need transport. Some great boat tours leave from Laem Sai pier, including cave canoe trips (recommended). Owner very pleasant, speaks reasonable English. As far removed from most peoples perception of Phuket as you could possibly get. Laem Sai resort in on a quiet road that is well used by people from Thanyapura (cycling/triathlon etc).
Google Maps