Well steve, there is a great drive to Aberystwyth,
From Llandinam go to llanidloes, then llangurig, then to Aberystwyth, just before Aber you can stop at nant y arian to watch red kites getting fed, forest walks etc. I love this road, just don't push too hard, those bends can be sharper than you expect, take it steady and enjoy the countryside, I've never tired of that road. Mandatory to have fish n chips on the front, and Ice cream too.
From Aber take the north road towards Machynlleth, but if your smalls are small enough veer off to Borth for the Animalarium, tiny family run zoo type place, cheap to get in and very hands on, pet a snake or a crocodile(baby I might add) got a leopard and a couple of lynx too.
From Borth you can head to Ynys Hir, where you can park/drive on the beach, not too sure of dog rules there but its an ideal place for 'em. lovely veiw across estuary to Aberdyfi (go there another day too!) then on to Ynys Las where there is an Osprey project, with a hide, hi po binoculars and a nice boardwalk stroll (we spotted loads of lizards basking last year)
Then on to Machynlleth, or miss the above divertions and go straight to Mach from Aber, turn right at clock tower and head towards Cemaes Road, Carno (MY Village!) Caersws and Llandinam.
You could cut across from this road (take the mountain road just before you leave Mach, on the right
for a thrill) and go via Llyn Clwyedog (in fact do a lap of it!) back through to llanidloes and back to llandinam from there.
As I said before Aberdyfi is the jewel in our crown round here, lovely old seaside town, very restrained and laid back, you can walk for miles on the beach (I think with your dog to, certainly in places) and the road from Mach to Aberdyfi is, well words fail me, the run along the estuary is twisty, and up and down hill, you'll never be able to get up to the speed limit in places, and when the sun shines on Aberdyfi....
Also if you want scenery, turn left at llangurig, and trek down to Rhayader, then (nose about the town first if you like) head right to Elan Valley, stunning, truly stunning. This is red Kite country too, I was working in Rhayader and lost count at 20 red kites circling overhead, very low overhead, again there is a feeding station here.
Oh and as to pubs, you can always come to Carno, and the Aleppo Merchant Inn (Home
) I wrote their website for them, earned me a round of drinks one night lol. they got a nice garden if the weathers nice, and well behaved kids are OK there (mine love climbing the tree in the garden)
I like the Italian in Newtown too, La Terrazzo I think, not the most authentic, or greatest food, but a nice feel to the place.
I'd also recomend a day out to Ludlow from here, great place, great riverside walks (or hire a row boat) explore the castle, and the old medieavel town, there is a route through Clun that is stunning to drive, let me know if your up for it and I'll detail it more.