With preferences and budgets varying so hugely, I would never be so bold as to tell anyone where to stay. All we can do is to stay at as wide a variety of properties as possible across the hospitality spectrum and present our findings, trying to view each property as objectively as possible and, hopefully, through the eyes and mindset of the sort of holidaymaker who would consider that property in the first place.
Because the focus of your holiday is diving, your choices are severly limited. For more advanced divers, Speyside, up on the hilly Atlantic Coast is the place to be - but there are virtually no rental houses/cottages in that area and no "town" to speak of. Therefore, you will probably need to look in the more popular, but flatter, southwestern tip of the island.
Your best bet would be to have a really good study of all our dive section (menu: Out & About > Activities/Things To Do > Diving) which will give you a good backround. Then, choose your dive service. Then choose your accommodation.
Wherever you are, a rental car is essential if you are to get the most from Tobago. There are exceptionally few rental properties (or even guest houses or hotels, that are within easy walking of many shops, restaurants and other features).
Have fun. The more effort you put into research now, the more successful your holiday will be.