I was in phuket early this year. If you're on a budget, I can recommend Casa Jip, guest house located in Patong.
Its near the bars, mall, and patong beach.
If you want a budget resort with pool, you can also try Jang Resort.
For island hopping tour, I still have the contact number of phuket tour, their package includes airport transfers, roundtrip and
phiphi/maya bay tour with lunch. City tour can also be requested. I can send you the number if youre interested. I think we got it at 2000 baht, my friend got it at 1800 without city tour.