what are must sees in northeastern Spain?

Zaragoza (between Barcelona and Pamplona) is a worthwhile stop for most... This being said, it is the only large Spanish city that I have never visited, so I cannot say much more!
Continuing from Pamplona towards the ocean, the Basque cities of Bilbao and San Sebastian are very interesting locations, too.
Around Pamplona, you could consider a side trip to Olite, where the Palacio Real is both stunning and undervisited.

As for Barcelona must-sees, this very website has some tips in the Explore Europe section (not the forum). A day definitely won't cut it: make it two full days at the very least, and preferably 3-4.

My must sees and yours are probably different. There are many small towns worth visiting as well as outdoor areas, but without a car most are probably difficult to get to in a timely manner using public transportation.

Head right to Bilbao and Basque Spain. The Guggenheim, San Juan de Gaztelugatxe for Game of Thrones fans, Donosita-San Sebastian, a gorgeous coastline with charming villages all accessible by train and bus. Did I mention Pintxos? Brad

This is a July trip, correct?

I have been to Zaragoza and it's a great destination in general, but I wouldn't return there in July. It is likely to be brutally hot at that time of year--average high excluding the years 2011-2023 (which one assumes have only been hotter) is reported by Wikipedia as 90F; the record is 112F. There's no need to subject yourselves to that when Pamplona is so close to the usually nice and cool Basque Country. Coastal Catalunya would also be a much better bet than Zaragoza in mid-summer.

Oh of course, missed that it was a San Fermín trip. Zaragoza can indeed be scorching!