Good question.
Maybe we can backtrack a bit, and find out how many people you're going with and what they ages are!
For instance, we're a family of 3, and my son is turning 4 end of May.
If we went in for MM that means we get into the park an hour before regular opening (have you checked out the calendar on disneyland.com to get the hours?), and if we had the very light breakfast, we could probably make it to the last seating for Minnie's, as more of a brunch than a b'fast. I would imagine, just going by other character b'fasts, that the last seating would be around 11 or maybe 11:30.
You're well within the 60 days that you can make Priority Seating arrangements (sort of like reservations), so you can certainly call Disney Dining to find out what their last seating would be.
But if your family gets hungry early (if they are school aged so have had a nice meal before going off for the day, rather than a 3 year old snacking when he wants, LOL) then it might be best to get the earliest seating...but by doing that you have to be aware that you're giving up prime park touring time...it's much quieter in the early mornings for riding rides.
As for days...I love weekdays, they make me happy. The park opens a bit later so MM is later (I am a nightowl and only at Disney am I OK with waking up early, but later is still better for me), the weekenders have mainly gone home.
MM days are Sunday, Tuesday, Thursday, and Saturday, so it looks like your MM would be on Tuesday.
I've asked more questions than answered you, but thinking things like that helped me start to plan, so maybe it'll help you too.