How far is Miyajima from Osaka? It's on my list for next year.
Miyajima is in Hiroshima, which is just a bit over an hour from Osaka by shinkansen. But then once you get to Hiroshima Station, you'll need to transfer to the normal JR Sanyo Line and head toward Miyajima, which is maybe a little under 30 mins. If you are based in Osaka, you could easily do Miyajima and the Peace Park in a day and then head back to Osaka that evening. That is, assuming you come really early.
I thought icoca was just suica now.
Also Ichiran sucks deal with it ( ≖‿≖
Nope, Icoca is still Icoca, at least it is here in Hiroshima.
And your opinion on Ichiran is insane. You are literally the only person I have ever heard to make that claim. You are like the Armond White of ramen. I don't doubt that you know a place that you consider to be superior, but Ichiran is fantastic and it is basically a must for every new visitor. It's cheap, it provides an interesting and novel dining experience, and the ramen itself is incredibly delicious.
Is it wise to plan the first trip to Japan from mid to the end of August?
I read that it is the hottest and of the rainiest months.
Not rainiest, but certainly the hottest and muggiest. I'm sure that people coming in August can still have a great time, but it would be wise to temper your expectations about the weather and come prepared. And it's not the heat that will get you, it's the humidity. I think I mentioned it in this thread, but I was born and raised in Florida, which is pretty much the hottest and most humid state in the US, and I find August in Japan to be absolutely miserable. This is mostly due to the fact that you walk a lot more in Japan than you do in the states, and also because most buildings are poorly insulated and don't use much a/c. Good for the environment, but bad for comfort. If you anticipate that you'll be drenched in sweat and maybe bring an extra shirt in your bag or something then you should be alright though.
Oh, and they sell these wipes at convenience stores called Gatsby (I recommend the Ice Type, which has menthol), which are basically wet wipes to wipe your face with. They feel great in the summer.