schumigirl has given you some good advise about where to start.
What you are asking is a bit vague and hard to answer, because it will come down to personal tastes...and whether the plan is to stick together or each go their own way. If you all like the same things, great, it makes it easier to plan.
June is a busy month, so:
1 day trip can be an issue without planning....or: Express Passes (Single or Unlimited)!
2 day trips are more relaxing and you have to stay somewhere...why not Onsite...at a Deluxe Hotel? A 1 night Onsite stay, at a Deluxe Hotel, gives you Unlimited Express Passes for 2 days...and you don't really have to plan anything...you are onsite and can walk onto any ride without much of a wait (if any). Very relaxing.
Wait! There's More!
Volcano Bay opens late May, so there is another option of things to do.
Does the family like water rides, but doesn't care about Volcano Bay? Wear your swim gear, anyway...ride the water rides and you will dry quickly in the summer weather.
You sure 1 or 2 days is all you have?
