Depending if new dog = puppy and so limits how far you want to walk. Cadair Idris might be a bit much! New Precipice Walk from Llanelltyd has gorgeous views and can be shortened (the full route is ~5 miles). +1 for Castell y Bere, hidden derelict welsh castle, in a beautiful quiet valley and start of the longer walk up Cadair Idris. A good short but quiet strenuous walk is from Cwm Bychan up the Roman Steps to the col (you can continue up the faint paths to Rhinog Fawr summit), amazing views. But quite a drive from Mach, although you could combine with time at Harlech Castle.
Don’t discount time at the beach. Aberdovey/Aberdyfi is a nice place. Tywyn and Borth are both typical UK ‘resorts’ but have big sandy beaches so even though there are dog restrictions in the town centres, you still have miles available. And you might see dolphins from the coast.
The ospreys should have returned to Cors Dyfi.
We’ve usually stayed at Cae Du for direct access to the sea, but it’s probably a bit far from Mach, and I hear it has got expensive.