South Downs without a car? (+ short England/Wales itinerary)

Bus service in Eastbourne is plentiful, it's not somewhere considered rural. You can easily hike Beachy Head, Cuckmere Haven and Birling Gap although be mindful that the Seven Sisters are the most strenuous part of the South Downs Way walk.

You don't say where the conferences are taking place. You don’t see the Seven Sisters by walking on top of them. Good view from west of Cuckmere Haven.

Cardiff:> see Cardiff Castle; Caerphilly Castle - short local train ride N. - wonderful medieval castle with moat but the town is a dump.
St.Fagans Castle & Museum = about 7 miles W of Cardiff city centre - Cardiff bus 32. Needs at least half a day. Also see Cardiff’s waterfront (bay) about 2Km S of centre. Castell Coch is worth a look but a bit off a hike up a steep hill from Tongwynlais on the N side of Cardiff.

Ah, just added -- conferences in London and Cardiff.

St. Fagan's is one of my favorite places I've been-it's a must see and there is a bus from Cardiff-I think it used to leave from the front of the Holiday Inn.

It is very doable as I did just what you are proposing last month. I spent 2 nights in Eastbourne before heading back to London for 5 nights. In hindsight, I would have spent another night or two in Eastbourne. Eastbourne, itself, was a nice enough town (beach, pier, pubs, restaurants a plenty) and a lot of British folks on holiday. On my lone full day, I hiked from my hotel (The View Hotel, which I would stay again when in town) facing the sea to the SDW. I passed Beachy Head, Cuckmere Haven, Birling Gap, then turned inland and walked through the Friston Forest while getting a nice view and photos of the Litlington White Horse. Quick lunch and a couple of ales at the Longman Brewey complex and The Plaugh and Harrow Pub in Polegate. Then, another mile or two to my destination: The George Inn in Alfriston. I cannot recommend The George Inn enough (built in the 1300’s). Alfriston was a cute town in and by itself. From there, I took a bus from right in town to Seaford, then the train back to Eastbourne. In all, it was about 13 miles of great hiking, but you could shorten (or lengthen) it to fit your fitness level or desires.

It can take nearly 3 hours to go by train from Cardiff to Tenby. You could buy Advance tickets for £13.50 one way (specific train) or off-peak returns for round £36 (non specific trains). Cardiff to Bath is just over 1 hour and trains are hourly.https://www.traintickets.com/?/

The south coast of Pembrokeshire west of Tenby has spectacular cliffs and bays but can be difficult to reach without a car. You could go down to the harbour and take a boat trip. Caldy Island is worth a visit. After a whole summer of hot sunny weather, it looks like the weather will change this weekend for Low pressure and some welcome rain as most of Wales & England are experiencing drought conditions. October can have good weather but may also likely to be wet. Tenby is a beautiful harbour side town with lovely beaches on all sides but won’t be much fun if it is raining. https://www.visitwales.com/destinations/west-wales/pembrokeshire/things-do-tenby

Another place you might like to consider when in Cardiff is train to Chepstow and walk down the hill to see the castle and world’s first iron multi span bridge over River Wye. Then bus to Tintern to see the ruins of the Abbey built in the 1100’s. This area is wooded and the trees will be turning colour in October.
For buses :> https://www.traveline.info/