Unfortunately I couldn´t find the guide books we used for our excursions. We were there in 2004 so things may have changed a bit...
Our memories aren´t very detailed (and we disagree on a few points) but some of the hikes we remember include jogging on the northern edge of Lagoa Azul - one of the twin lakes on the western part of the Island - with nice views down into the old volcano crater.
We were also hiking around Lagoa das Furnas (apparently temporarily closed) and visiting the hot springs in Furnas, some with water to swim in - if you can stand the smell - and also bubbling sulphur springs in the vicinity.
We had a rental car and thus no problems getting around. The local buses seem to be less reliable and not very frequent (compared to Madeira where the buses were a great way to get around).
I´m sure you can find the same information on your own, but this website
is what I found trying to refresh my memory.