The data comes from the states and then goes to the CDC or HHS, wherever they are sending it now. I’m not sure if the reporting goes from the hospital simultaneously to the CDC and the state level, or if it first goes to the state and then up to the CDC. I assume it is all simultaneous, because it all seems to be available daily. I could be wrong.
People seem to want the data to be perfect, but it is not perfect. Flu data is imperfect also. Things get adjusted after the fact. It doesn’t matter, it just has to be close enough. During flu season there will be even more inaccuracies, because if a test result was inconclusive (that happened to my girlfriend’s husband) and flu test was negative, but the person presents with pneumonia it will be a judgments call. Covid does seem to have a different lung xray than flu from what I have heard on TV, so that will help I guess. Pneumonias not tested for flu wind up in flu data very often, which people have argued for a long time is overstating flu numbers. Depends how the pneumonia happened, but still the point is there are inaccuracies and if you look at flu burden data from prior years you will see it is an estimate, a range.
A lot of people like the Johns Hopkins site. Another popular one is Worldometer You can scroll down and go to the country you want. Once on the country you can see today, and then also click on the tab for yesterday to see both at a glance.
For my state I look at the state website and also an additional website that was created by the woman who was fired by my governor. Both have tons of data updated daily. Positivity rates, how full the ICU’s are at every hospital in the state, case by county and by city. Deaths by county. I would assume every state has something similar. The one thing I don’t see is how much the hospitals can grow their ICU capabilities. For Instance I heard recently Dade County is at 147% ICU, so that to me means they have created new ICU units in some hospitals above and beyond their typical capacity.