2nd time itinerary

Will be returning to Japan in May/June if travel restrictions are lifted. Spent 2 weeks in Tokyo and Kyoto with day trips to surrounding areas. Considering the Northeast areas and also Okinawa and Osaka. Have 14-16 days to travel.

It really depends on what you like. How much do you like moving around Japan or do you want 2/3 main areas to stay and complete day trips from there.

A bit more on your interests and what stuff you like to do is really needed before suggestions are made.

Some basic suggestions are here: https://www.japan-guide.com/e/e2400.html

Certainly loads to see in both places - though as stated you need to flesh things out more. For Okinawa, how much time are you thinking of spending? And are you fine with the main island or want to see others as well like Miyakojima and Ishigaki? What are your interests?
For the Northeast, I presume you mean the Tohoku Region - again, how much time and where? It is a very large area.
I suggest you also consider getting the ANA Experience Japan Fare, or JAL's clone of it, or if convenient enough, a low cost carrier like Jet Star or Peach.
https://www.ana.co.jp/en/us/plan-book/promotions/special-fares/
The Tohoku Area Pass might also help you a lot.

I'd probably go for the northeastern Japan as May and June is quite warm in the south. Instead of arriving Tokyo, maybe see if you can arrive in one of the airports up in the north.
For northeastern Japan, you can't miss out on Oirase Gorge. Chosen to be one of the most stunning places in the country. You can get to the gorge from Aomori, sightsee your way through to Lake Towada.
https://visitjapan-vegetarian.com/oirase-gorge-discover-the-most-pictu...

Another spot up in the north in Iwate prefecture is the Geibikei Gorge. Taking the traditional boat ride down the gorge enable you to enjoy the scenery + cultural element from the traditional song sung by your boatman!
https://visitjapan-vegetarian.com/geibikei-gorge-and-the-most-scenic-t...

The gorge isn't too far away from Hiraizumi, which is a town with rich historical and cultural elements that I highly recommend you to drop by if that is where your interest lie as well.
https://visitjapan-vegetarian.com/the-most-scenic-temple-tour-in-hirai...

Spent 2 weeks in Tokyo....
Then you can visit Tokyo university located in meguro ku by keio Komaba Todai mae station

May / June isn�ft generally yet that hot, so there is no NEED to go to the North. But obviously it is nice there.
With only 2 weeks I think you need to decide if you want to do a more traditional first Traveller type trip with Kyoto, Osaka and Tokyo (and places around). Or if you want to do something a bit more unusual eg Okinawa and a bit less of Honshu or Tohoku and a bit less of Kanto/Kansai area.

It really depends on your interests. Hiking? Old temples? Anime? Shopping? Nature? Big cities?