Its here, because I’m looking for reasonably thought out speculation; knowing that there isn’t a factual answer.
Do any of you have a somewhat informed thought on when:
Yellowstone will reopen?
It will be substantially repaired to have good experience?
I’m going in September…or at least that was the plan
I’m reading that parts of Yellowstone will open shortly. The area around Old Faithful, for example, is relatively unaffected. But much of the northern park will remain closed indefinitely. The park’s capacity may be limited until the roads are repaired, which won’t be anytime soon. September will be substantially impacted.
Here’s the latest update from the park:
One of my favorite parts of Yellowstone was Lamar Valley, where you can see all kinds of wildlife. Looks unlikely to be open in September.
Road through Lamar likely closed for summer '22 | This Just In | jhnewsandguide.com
Northern part of the park will likely be closed for the rest of the summer. Not sure if any of it will reopen by September.
Are you staying in or outside of the park? Even with a reservation in the park your ability to enter may be changed or restricted. Outside the park your accommodations may be affected as well.
I have friends who live about 40 miles north of the Park’s north entrance. They believe this entrance will be effectively closed for at least a year due to many areas of substantial damage to Route 89 (connects Livingston to Gardiner and the north entrance).
The most difficult and expensive repairs will likely be in Yankee Jim Canyon, a section of the road about 9 miles long that begins 6 miles north of Gardiner. Here, the confined terrain constrained & intensified the Yellowstone River’s flow, allowing it to carve away impressive amounts of the road. Repairing these sections (that are more or less perched along the canyon’s walls) will be a formidable task.
There are more updates in the NPS link above. Plus some analysis from here: Yellowstone National Park May Not Reopen This Season — What to Know If You Have a Trip Planned
In the meantime, the NPS and Yellowstone National Park Lodges have asked all overnight visitors to leave both lodges and campsites. A spokesperson for Yellowstone National Park Lodges told T+L the group was “contacting all impacted guests with reservations by email and text and providing them guidance.”
As of Thursday, all entrances to the park remained closed, but the NPS said it was possible the southern loop would reopen by Monday, Jun. 20.
I was actually in Yellowstone from Saturday through Monday. It was our first ever visit. We had planned to stay though Thursday but it got cut short.
Saturday evening we arrived at our hotel, everything was fine. Sunday it was pouring rain all day long. Nevertheless we carried out our planned itinerary and went to see Old Faithful. If anyone asks, yes, the geysers still operate even in pouring rain. 
Monday was beautiful, so we thought great, finally we can really start to enjoy the sights. We drove up from West Thumb towards Canyon Village, stopping for quite a while at Mud Volcano. A ranger we passed said the road was closed to Canyon Village, we said ok we’ll go as far as we can then turn around. So we got to see the Upper Falls from the South Rim of the Yellowstone Canyon.
Then we drove back to our hotel, getting there around 6:30 pm. Ten minutes after we got there our room phone rang. It was the manager, telling us he’d been trying to reach us all day, saying the park was being evacuated and we had to leave immediately. So we packed up and headed out, greatly disappointed.
We left through the West Entrance. Fortunately, and surprisingly, it was not hard to find a vacant motel room in West Yellowstone.
There’s an guy who works in Yellowstone who has been giving “inside the park” updates on his youtube channel, Park Junkie. Pretty interesting to see Old Faithful and the Grand Prismatic Spring with nobody else around.
It looks like thinks will be opening up quicker than anticipated.