The Whitney main trail would be a challenge for 7 people who do not hike regularly.
Does it need to be a 14er? With a group of that size and experience level, it is possible one or more could get sick at higher altitudes, meaning you will need to make decisions or sticking together or splitting up the group.
I highly recommend hiking in the Lake Tahoe area. Many summits to choose from with incredible views and reasonable mileage. Also lots of stuff to do at lake level for non hikers.
Early June could require ice axe/crampons/self-arrest skills if you want to climb the tall peaks in CA this year. The southern Sierra snow pack is currently at 197% of average!
