We have been thinking to make a whistle stop in Ireland - 26 September (when we arrive from South Africa at Heathrow) to 28/29 September.
We would like to see Dublin and Galway. However, it would have to be very cost effective (read Cheap).
My thoughts: Fly Heathrow to Dublin. Sightsee Dublin 2 or 3 highlights on that day. Take a late afternoon bus to Galway. Overnight in budget accommodation or B&B. Sightsee Galway and possible boat trip around islands off the shore. Fly Galway to Edinburgh. Then possibly fly Edinburgh London. Is this realistic or should we forget it.


Is this realistic or should we forget it
Forget it. It will cost you a lot of money compared to what you'll get for it in return. Spend the extra days (and your money) in the UK instead.

I suppose it is possible but whyunless you are a fan of hanging around airports, like sleeping on cross country coach services and being exhausted at the end of the process.
Take out a piece of paper and write down your itinery and see what I mean. You will not find me on this trip!
R

It can be done, but might not be worthwhile. Keep in mind that if you are traveling from South Africa and sightseeing in the same day, you will definitely be jet lagged. This will drag you down even if you spend some time in London first.
Re: Dublin to Galway. To save time, it would probably be better to take the train. If you book your tickets online you will save a lot. Also make sure you get to Galway at a reasonable time as most B&Bs are family run and don't stay open late. You will probably also want to check out Galway's nightlife (if you have the energy!!) as there is great trad music in the pubs.
The sites in Galway are actually quite few in number, and a trip to the Aran Islands could take most of the day. Lots of things close early, so check hours before you go.
Also... remember you'll be wasting 2-3 hours in the Galway airport. If you want to do this trip, 3 days would be better...

Keep in mind that if you are traveling from South Africa and sightseeing in the same day, you will definitely be jet lagged
Err, the time difference between South Africa and the UK & Ireland is only 1 hour...
But yeah, I catch your drift - I wouldn't fancy a whirlwind sidetrip to Ireland right after a 10+ hour flight.

From Heathrow, you could make your way to Luton airport
and take an AERARANN.COM / .....direct flight to
Galway.

I had a feeling the time difference wasn't significant, but I actually met a woman from SAfrica when I was in Ireland and she dreaded the flight back :) Thanks for the clarification, though!
Oh, a whistlestop--basically--just shows you where the whistles and stops are.
Relax and enjoy Dublin. Pub music crawls, an amazing trek just outside Dublin that leads you right back to Johnnie Fox's, a venerable pub. Grafton Street, Trinitiy. Just walking and exploring and breathing and getting a sense of place that's unique.
Make the west another trip, and you'll get more out of your total experience.
Enjoy the journey!
The Crew at Authentic Ireland
I wouldn't listen to Aribo if I was you. You need to make up your own mind from what we tell you about what you can do. First of all I would say travelling to Dublin for 2/3 days is very realisitc. You can easily get cheap flights from any London Aiport to Dublin. There is plenty to do in Dublin for a few days.
It is also realistic to visit Galway and I agree with Jengaza, if you are travelling to Galway you should take the train. There are 8 trains daily on the route and it will save you about 2 hours. In saying that a return ticket costs around 35 euro which is a little more than the bus.
Lastly flying to Edinburgh from Galway is realistic if you have money. Flights for 2 people to fly from Galway to Edinburgh could cost 120 euro per person one way. What you could do is get the return train back to Dublin and fly from Dublin to Edinburgh. Flights with Ryanair are very cheap and will cost you only around 40 euro.
Hope that helps :)