This is nearly perfect. These are some very minor points that will help you sound more native.

It Was Amazing!! (capitalize titles)

August 27th
Today is a little muggy.

Yesterday, my old friends and I went to Asakusa and watched a rakugo! (comic story) We wore yukatas. :)

* Are your friends elderly? If they are your age, but you've been friends with them forever, you could say "long time friends". Or you can just call them friends.

I didn't know that rakugo is really so interesting!!

* "Really" isn't incorrect here, but it sounds more natural with "so". If you want to use "really", you could cut off the first part. "Rakugo is really interesting!!"

Then, we took photos in a purikura (photo booth)* and stayed at a luxury hotel! We ordered the a meal through room service...! We really enjoyed our holiday!! But I have to save money next month. *.*

*or "Then, we stepped into a purikura"

the meal / a meal — either is ok, but it sounds more native with "a meal" in this context.