Have a look at the walks proposed by the Wales Tourist Board Official Site
http://www.walking.visitwales.com
Visit the following website, where you can find self-guided trails in Wales.
http://www.wales-walking.co.uk/walking-trails.htm
From Penrhiwgaer, a wide range of walks is available. The following walks are examples of the sort of walks you will find, starting with the closest.
Bwlch Nant yr Arian Forest Centre
Elan valley
http://www.bbc.co.uk/wales/mid/sites/reserves/pages/elan_valley.shtml
Hafren Forest
http://www.llanidloes.com/hafren_forest
Llyn Clywedog
http://www.llanidloes.com/clywedog