In Bangkok, I stayed at the CityPoint Hotel. This centrally located hotel was convenient to the train and other forms of public transportation, food and action. The rooms are clean, comfortable and the stay was inexpensive. I think it cost me $50/night. You can't beat the location and it's definitely a great budget friendly place to stay.

In Phukhet I stayed at the Nap Patong hotel. This beautiful, boutique hotel is really nice and a block away from the beach. It's super far from the airport though, like 2 hours but it's very clean and again, close to the beach so either way, you want to make the journey from the airport so you can chill at the beach.