Plenty of people in many states going to bars in the past couple of days with barely any precaution according to what I've seen in the news and on Twitter (YMMV).
There will be some sort of rise in cases, but that rise will be mitigated because of some level of social distancing and an immense increase in mask-wearing versus a "normal" baseline. Like, I'm in Chicago and I don't know a single person who's going back to their office anytime this summer. That means they aren't commuting, aren't around other people all day, etc.
A NYC-like spike isn't going to happen anywhere unless people get super complacement.
Hopefully there are no significant spikes (and certainly no NYC-like ones), but it will be a minor miracle if reopening doesn't cause a significant increase in cases in a number of places.