It should depend on the situation in September, but school should definitely reopen before most other public spaces. The fact that some states have jeopardised full reopening by opening bars and restaurants first is scandalous. Education is more fundamental of a right than dining out.
That would be true if reopening a restaurant was remotely similar to reopening a school, and if kids were not getting educated at all. Classes will be held, just in a different mode.
I am for things opening up, even if cases inevitably increase, as long as it is balanced with healthcare capacity. But schools or any other environment full of children should be among the last places to open back up.
Of course there is a difference in opening restaurants and it is somewhat easier. But online schooling is nowhere near as good as the real thing and in particular increases educational disparities between the wealthy and poor, as well as being hugely detrimental to kids who have an unstable and/or abusive home. Some effort has to be made to have pupils in at least some of the time. Furthermore, while the scientific jury is out as to whether children can actually spread coronavirus or not, there have been very few (if any) outbreaks linked to schools in countries where they have reopened.
Here in the UK, restaurants and pubs were not reopened until last week, despite the fact that cases are far, far lower than in most US states where they were reopened a while ago (and despite the UK’s response being one of the worst in Europe). On the other hand, though, all schools are, barring a major spike in cases between now and then, going to reopen fully in September.