Lake Tazawa (田沢湖) is the deepest lake in Japan (423 m) with the bronze statue of the legendary Princess Tatsuko standing on the western shore being a symbol of the lake. The great help was provided by this website, where I found all the information I needed in English. The Tazawa-kohan bus terminal near the lake is about 15-20 minutes by bus from Tazawako JR station. There are also rental bicycles available and to hire one was my initial intention. However, given the very limited time I've had - I decided to take a taxi from the JR station to take me around the lake and to stop at all famous sights. The ¥12,000 that I paid were absolutely worth it - I, honestly, do not see how one can ride around the lake in "1.5 to 2 hours", as some websites suggested... Unless you are pedalling like mad without stopping, probably... The use of the taxi not only allowed me to see everything I wanted but also allowed the time for the ride on a cruise boat (operates four times a day from Shirahama, near Tazawa-kohan bus terminal) - so I actually managed to see Lake Tazawa sights twice: both from the shore and from the lake.
Please note that this was the longest distance I've travelled in one day and to get to Tazawako without a JR pass it would actually be cheaper (and, of course, faster) to fly from Osaka to Akita, followed by only one hour travel on shinkansen. As I did have a JR pass - this day has also presented an opportunity to catch up on a lot of work...