My suggestion is stay 1 night when you first land then fly out the next day to Phuket(bear in mind it is the monsoon season in June over there so you might want to consider that factor) to spend a few days and then fly to Samui (good season to go in June) for a number of days. If you still want more adventure, gte back to Bangkok with 5 nights to go, spend 2 of which in nearby Kanchanaburi and the last 3 nights in bangkok. Make sure the last 3 nights in bangkok are across the weekend so that your girlfriend can go shopping at Chatuchat market !

Get about by budget air lines like air asia etc.

have fun in beautiful thailand