Hi Carle
It's pretty difficult to give you upright answers to your questions.
For the cost, JR East offers various passes: 5-day, 10-day and 4-day Flexible.
http://www.jreast.co.jp/e/eastpass/prices.html And of course you can also use the nation-wise 7-day, 14-day and 21-day JR Rail Pass if you want to combine your Tohoku trip with other places you want to go in Japan.
http://www.japanrailpass.net/eng/en003.html Using the following you can work out the train schedule and cost of each journey and see whether a rail pass comes out on top or not
http://www.hyperdia.com/cgi-english/hyperWeb.cgi Of the places I mentioned, most of them can be reached by taking JR. They included Matsushima, Yama-dera, Hiraizumi, Aizu-wakamatsu, Inawashiro-ko, Kitakata, Ishinomaki, Tomizawa Site Museum and Mitsui Outlet Park.
In Hiraizumi, you can ride the town loop bus (300 yen) to get to Motsu-ji and Chuson-ji. Also in Aizu-wakamatsu, you need to ride the loop Town bus (500 yen) to get to various sights. For Ouchijuku, from Aizu-wakamatsu you need to pay separately to ride the private scenic Aizu Railways (
http://www.aizutetsudo.jp/index.php) to Shimogo followed by 10-15 min taxi. From mid Apr. to late Nov. there is a direct bus to the village from Aizu-wakamatsu. In Inawashiro-ko, you still need to take a bus to get to the lake and the Hideyo Noguchi Memorial Hall. To go to Akiu Onsen, you take a bus from Sendai. For Zao Onsen, in skiing season, there is direct bus from Sendai. At other times, take JR to Yamagata, then a bus to Zao Onsen, from the town is cable car to Zao-san and the Okama-ko. BTW, note that road access to Okama-ko is closed during winter time.
As for how many days, it's even more difficult to say. It depends on individual preference and pace of travelling. For a whirlwind tour, yes, all the places can be done as daytrips from Sendai if you don't mind a lot of travelling on the train each day. The question is whether that is what you want in your vacation. It's only natural if you want to see as much as possible in as short a time as possible, esp. if it is your one and only trip to Japan. That's what I did when I first visited Tohoku. I did Yama-dera in the morning and Matsushima in the afternoon. Half a day for Yama-dera is OK, but half a day for Matsushima is a bit rush. Now Matsushima is on my itinerary again for my upcoming second trip to Tohoku, and I wish I had used the half-day last time for somewhere else! And because of that, do excuse me for being hesitant to say how many days are needed.
IMHO, visiting Tohoku requires a bit more planning. It's unlike other popular destinations like Tokyo and Kyoto where you can always go anytime of the year. Tohoku's beauty varies with seasons. To give an example, Ginzan Onsen is popular during autumn foliage season and is also beautiful during winter with snow, but I have read negative comment of the place being smelly during hot summer months. By all means do go to beautiful Tohoku, before it is being over-flooded by tourists. There are a lot more places to explore than those that I have mentioned.
