Going through Miyagi:

(I am assuming you have seen most of Sendai already so I wont include it)

Matsushima Bay - Pretty self explanatory

Ishinomaki Mangattan Museum - Museum dedicated to Ishinomori Shotaro (Kamen Rider, Super Sentai, etc.)

Iwadeyama - Some Date Masamune related buildings

Naruko Onsen - I recommend Shintoronoyu if you only are passing through or Naruko Hotel if you are staying the night

Naruko Gorge - Large canyon with a nice view.

Mt. Kurikoma - Better in fall with the autumn leaves, but still nice and it should be a fun drive if you are into that.

Iwate:

Safari Park, New Zealand Village - These are attractions more aimed at kids, but might be fun if you like animals.

Hiraizumi - Famous temples, shrines, and old buildings.

Morioka - Nice, quiet city with awesome food. Aside from the famous wanko soba, reimen, and jajamen, I recommend Sanzushi, a fairly famous sushi place that is known for nattomaki. Its located around the red light district/business hotel district.

Kenji World - An indoor water park and onsen. Hawaiians in Fukushima was better, but it was still fun.

Akita:

I honestly have no idea, aside from onsen, food - kiritanpo nabe, yokota yakisoba, and hatahata -, and akita bijins.

Aomori:

Hirosaki, Aomori - the Sakura Matsuri runs through Golden Week at Hirosaki Castle and is definitely worth a visit. You may also still be able to get your hands on some awesome hirosaki apples. If you stay in Hirosaki, you have to book a hotel now (or, ideally, last year). I would recommend staying at a penshon where you can get a taste of gourmet food made with local ingredients (probably apples).

Aomori City - lots of museums and an aquarium.

Oirase Gorge - Never been, but have heard its nice.

It might be nice to drive north through Miyagi, Iwate, and Aomori and return south through Akita and Yamagata, just so you can see everything.