I teach, so I am usually SAHM during the summers. We do have a routine of sorts, but it is very fluid and will change based upon weather or the whims of the family. This is generally what we do:
6-7 AM - wake up - My son is an early riser, usually by 6:15 at the latest. It doesn't matter if he goes to bed at 7:30 pm or 10 pm, his internal clock wakes him early. My daughter will sleep a little later, so he usually just does something quiet.
7:30 - breakfast and some TV or ipad time while I do the things I need to do (pay bills, etc). We also start any laundry we need to.
8:30 ish - family chores (we have a chore list, kind of Fly Lady style, where we do one chore per day and then a pick up of the kitchen, so we don't have to spend an entire day cleaning) When the kids finish they can have free play until everyone is done.
9:00 ish - we will run errands. If our errands involve stores that get busy, we often will switch this and do it before chores. It just depends on what needs to be done for the day.
10 ish - gym. The kids go to Kid's Club and I get my sanity in.
noon - lunch
After lunch - "school" - my kids do a school worksheet (math for my son, age 7, and writing for my daughter, age 5). We also read during this time. I agree with lots of others who bash e on this that summer is for fun, but as a teacher I also see the ramifications of no "practice" at the skills they have learned in school. I don't ask them to do hours of stuff every day, just a few minutes to keep them from losing everything.
2 ish - by this time we are usually at the pool and stay there until we head home for dinner, between 5 and 5:30. If the weather isn't cooperating we do something crafty, play a game, the kids will have playtime, or screen time.
6 ish - dinner, then normal bedtime routines (showers, shows, stories, songs, bed).
We also have time for whatever activities the kids have. They both are in gymnastics, my son is in an art class, my daughter is in dance, and we go to the library at least once a week. It just varies based on what we have going on, and on rainy days. I know lost of people aren't fans of schedules during the summer, but for us it works. :)