JR pass vs JR East Tohoku pass:
If you are utilizing only three days of travel using the passes, I would suggest getting the JR East Tohoku pass, as it is cheaper compared to the JR pass (7 days) and you have mentioned that you are visiting places only in Tohoku region.
JR pass - 29,110 yen (7 consecutive days)
JR East - 19,000 yen (bought outside Japan), 20,000 yen (bought in Japan) - 5 flexible days within a period of 14 days
JR East Tohoku pass coverage:
For some of the places that you have mentioned, either of the passes will cover only the partial routes. I can only talk about the JR East Tohoku pass, as I haven't used the JR pass in Tohoku. I assume you are starting from Tokyo:
Geibikei Gorge - fully covered
Lake Towada - fully covered (Also both JR buses - Hachinohe to Towadako, and Aomori to Towadako are covered in JR East Tohoku pass)
Lake Tazawa - fully covered (the short bus ride from JR Tazawako station to the lake is not covered by the pass)
Aomori, Hirosaki castle - fully covered. You'll still need to get a local bus or walk to reach Hirosaki castle from the station.
Ginzan onsen - the bus ride from Oishida station to Ginzan onsen is not covered by the pass.
Accomodation:
Personally, I cannot comment on accomodation, as all the places mentioned are scattered all over Tohoku, and 3 days is too short to visit all these places. Also, waiting times for local trains and buses in Tohoku are more (from what I have experienced). Realistically speaking, shortlisting to only two or three places could work. But if you would still insist, Morioka is a good base for day trips to Tazawako, Geibikei gorge, and Hirosaki castle. Towadako and Ginzan onsen will take longer to reach from Morioka, and are not ideal day trips from Morioka.
Also, please note that the JR buses from Hachinohe station to Towadako are suspended from November 12,2018 to April 19,2019:
http://www.jrbustohoku.co.jp/route/detail/?PID=9&RID=13A sample itinerary:
Day 1: Travel from Tokyo to Geibikei gorge. If time permits, visit any of the temples in Hiraizumi (Chusonji or Motsuji). Then travel from Hiraizumi to Morioka for the night.
Day 2: Morioka to Tazawako day trip. And back to Morioka for the night.
Day 3: Morioka to Hirosaki day trip. Then, travel from Hirosaki to Tokyo.
Resources online:
Check this link for more details on coverage areas -
https://www.jreast.co.jp/e/eastpass_t/Check this link for train schedules and travel times -
http://www.hyperdia.com/en/