There are many day-trips to the volcano. Most will collect you from the quayside for a run to the crater and straight back again.
If you want to see the quiet villages of Nikia or Emborio on the crater rim as well (and the view from Nikia in particular is terrific), you may need to make a few enquiries - there are a few guides who go a bit further, but not many!
Alternatively, there is a limited bus service into the interior.