There are some Sakura specialists on this forum, but instead of Aomori, you might want to look into places in the Japanese Alps instead.
E.g. per the current forecast Takayama has best viewing from 17th to 25th of April: https://www.japan-guide.com/sakura/
So you could to a tour like:
Day 1: Tokyo
Day 2 (that should be about 27/April, right?) : Takayama (or somewhere else in the Japanese Alps, check out if there are other places, e.g. somewhere in Nagano prefecture).
Day 3: Osaka/Kyoto/Nara, stay there as long as you want
Last days: Tokyo
That would be a much more compact itinerary
Otherwise if you go North, you might want to consider Kakunodate. It is a nice village/town in itself and you can reach it by Shinkansen from Tokyo. Aomori city I dont think is a specially beautiful place. You could actually modify your itinerary and do:
Day 1: Tokyo
Day 2 (or later): Kakunodate
and then continue exploring Tohoku, e.g. by visiting Hiraizumi (instead of Kyoto), maybe Tono or some nice onsen at Towadako?, some more hanami in Kitakami, Nikko (instead of Uji) and then come back to Tokyo and spend the last days in Tokyo (or do all the travel at the end and do Tokyo at the beginning. I.e. in this proposal you would completely skip Kansai and replace it with much less visited, but also nice places in Tohoku area. Just to make your trip more compact.
If with "Aomori" you mean Hirosaki, that would also be a very nice place to see sakura, but it is a long trip from Osaka (or from Tokyo), so you should consider flying from Osaka to Aomori. The good thing about visiting Hirosaki (or Kakunodate) for Hanami is that these places are interesting also regardless of Hanami. So yes, you can enjoy the flowers, but it is not only flowers, there is something for other people in your group as well, or if the weather isn't so nice, you can still do a bit of hanami and then do more "serious " sightseeing.
However I would go to Tohoku only if you can dedicate a few days to it. Tohoku is such a nice area that it would be a pity to just rush there for a few flowers.
And yes, Kyoto and Nara are also very, very nice places (I was in Kyoto this weekend and will likely go again next), but you should take advantage of your trip to Tohoku.
If instead you go the Japanese Alps route, it would be easier to get Tokyo, Kansai and cherry blossoms all in the limited days you have.
As a forth possibility you could do Kitakami as a day trip from Tokyo. A long day trip, but doable. It is about 3 h by Shinkansen from Tokyo to Kitakami, and the good thing is that the Cherry blossoms are very close to the station: https://www.japan-guide.com/e/e5077.html
Doing it as a day trip has the advantage that you could go a day that the weather is forecasted to be nice. (Although you are going to go during GW, so you need to think of seat reservation as well). Plus if some people of your group don't want to go, you could split and only a few go to Kitakami and others can remain in Tokyo.
So I think there are definitely possibilities how to do hanami at the end of April and combine it with a good visit to Japan.
Enjoy your trip!