A lot depends on whether you are 39mins north south or east of Aber!
Loads of good suggestions on here. The castle in Aber is good especially in winter ....you look out across the sea and get a real sense of how isolated it would have been. The cliff railway is brilliant - quick game of mini golf up the top. There is a camera obscura too and you can also do a nice cliff top walk toward Borth.
Further afield (south of Aber) you've got Dolaucothi Gold mines best Pumsant (it's NT) - the site of Roman gold mines / there are caves to go down and you can pan for gold which is a bit of a laugh.
North of Aber is the Centre for Alternative Technology at Machynlleth - fab place and well worth a visit. Lovely veggie and vegan food too.
Aberaeron is a beautiful Georgian harbour town just down the coast ....the beach is huge stones. Ice cream from the Hive on the Quay is a must (hopefully still open, not been able to get over due to Covid). Just up the road is Llanerchaeron (NT) a Georgian house set in a wooded valley. From there head to New Quay - take a trip out into the bay to look for dolphins.
Pontarfynach is a must.....the bridges alone are worth a look. You can walk round.....Jacob's ladder can be a challenge depending on your fitness/mobility. You can get the steam railway from Aber to Devil's Bridhe (or vice versa) and spend a couple of hours looking around.
There is the Cors Caron nature reserve at Tregaron - a huge wetland and big (paths are accessible). Then a quick look round the Welsh Gold Centre -she has some beautiful gold and silver pieces and a lunch by a roaring fire at Y Talbot in the market Square. If you're feeling brave (the road is narrow and windy) then take the mountain road out if Tregaron towards Abergwesyn ....it's an old drovers trail and the scenery is stunning.
mid Wales is a stunning part of the country - hope you enjoy it!