Hi Mandy
The Asa Wright Nature Centre is not on the north coast of Trinidad, If you look at a good map of Trinidad, you see a big road "Eastern Main Road" across Trinida with start in PoS, from West to East, you see the town Arima half way direction East, nearby the mountain area.
Piarco Airport as not so far from Arima, so a taxi or car organized by Asa Wright, can take you directly to the Centre.
The Centre is situated not far from Arima, in the mountain area. They also has an own website
http://www.asawright.org/ with a lot of information and many nice pictures. The Centre´s webbsite also has a road description and a basic map too, but I know that Tourist Information (in Trinidad) shall have more information too.
Laguna Mar is on the north coast of Trinidad. If you start in PoS, you drive via Maraval, over the mountain using the North Coast Road. You will pass some huge view points on teh way and the rain forrest is all the way up to the road. You pass Maracas Bay, Las Cuevas Bay, Chupara Bay and you arrive to Blanchisseuse, which is the end of Nort Coast Road.
It´s also possible to cross over from Arima using Blanchisseuse Road,wich you are using if you go to Asa Wright Centre.
But, that road isn´t paved all over and it also passing some areas where they use to have landslides sometimes during heavy rain. Do only use that road if locals tell you it´s safe to drive across the mountain. The North Coast Road is much better as it is bigger, and paved.
It is possible to stay over at Asa Wright Nature Centre, check their Visitor Information. And if you call Laguna Mar to make a reservation, I believe they can organize a driver with car to drive you across the mountain and later back to the airport.
Taxis has, like Tobago, fixed prizes from the airport to different towns/places, but I don´t know the rates. But that is something the Tourist Information in Tobago, at Crown Point Airport, should be able to help you with.
Ronald