Hi Suzanne, The end of August is a great time to go to Scotland. The heather is blooming and the Festival is on in Edinburgh. The latter has it's pro's and con's. If you go to Edinburgh in August with your eyes open and receptive to all the great things that the Festival brings to the city, then go and enjoy. The Festival is actually several Festivals at once. Go here to read about the different Festivals. Other than the film and jazz festivals they all over lap. I could have sworn that the film festival used to be in August too!
I've not been to the Tattoo, but I will someday! I did get to watch it on TV one year, but it has to be magical to be in the stands at the Castle.
So, the Tattoo takes place at the Castle which is at one end of The Royal Mile. Edinburgh is not a big city. If it were me, I would just plan on walking back to my hotel afterwards. Certainly, if you stay in Newtown, the Calton Hill area, Haymarket, or even Dalkeith, you can do it. I used to stay near the Royal Botanic Gardens and routinely walked home after dinner. It's generally a safe city. Here's a link to the bus schedules, but rather than try to decipher them, I would find a hotel and ask them about the transportation. Many, many of the people attending the Tattoo are visitors and so need transport. There is no parking at the Castle as the Tattoo is in the parking lot!!
I would recommend booking your hotel soon. But make sure your plans are firm. You will need to make a deposit and it may not be refundable. Also, you will likely need to commit to more than one night if you book on the week end.
As for the games, I've really only been to ones in the US. I have been to Argyle and it's beautiful and I would definitely not make a day trip from Glasgow. I would stay there. Here's the link to Undiscovered Scotland's page on Dunoon. I would book as soon as you decide.
Are you planning on renting a car? If so, there are some wonderful drives in Argyle. Also, you could plan on stopping in on one of the smaller Games on the earlier Saturday. It looks like Crieff have some the prior weekend.