East Hill is nice- Lovely old beech trees. You can walk along the ridge from above Ottery St Mary all the way to the end of the ridge overlooking the sea. It's rather nice.
Ashclyst Forest is good for walks through a mixed broadleaf/ conifer forest- not ancient but lots to see along the way. It can be very muddy after rain but there are lots of marked walks and a long bridle path all the way round with some good views over countryside.
Haldon Hill is very popular but I think it's mostly conifers.
Haldon Forest is lovely for a walk - lots of wildlife to see. The woods around Becky Falls are also lovely, although I seem to remember the entrance fee is quite high, but the drive to it is beautiful.