Ah! The perrenial currency question.
I've never known anyone refuse T&T currency, but have had some wide ranging US$ to T&T dollar quotes, even though they are supposed to be linked at a standard rate.
I think that most of the experienced Tobagophiles recommend taking some local currency with you for initial spending on groceries / taxi fares etc, say TT$1,000 max (around £100 or US$200) and then use ATMs to access cash as you need it for the remainder of your stay.
Check out
Money Matters in the
Odds & Sods section of the header bar for more tips and locations of the ATMs and Banks.
If your bank will arrange travellers cheques on a nil commission and return basis

then these are a good standby for any emergencies e.g lost credit card or malfunctioning ATMs
Cheers
Steve
Take only photos - leave only footprints. I like that concept.