Fruit picking in May-June

We are interested in fruit picking this or next month, Which area would be the best near Kawasaki/Tokyo?
We heard of this place in Yamanashi
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Is there any other better option? Also what would be the convinient mode of transport to that place, I have a drivers license so can drive from Kawasaki.

Any suggestions please?

I was hesitant to post a reply as I haven't been to any of the following. But in case you want to take a look, here is a list of fruit farms in Yamanashi Prefecture. There are 3 pages.
http://www.rurubu.com/season/summer/mikaku/list.aspx?KenCD=19

A rental car would be a good way to get to some of the hard-to-reach places. Note that most foreign visitor (with a few exceptions) would require a valid international driving permit on top of your driving license to drive in Japan.
http://www.japan-guide.com/e/e2024.html

Thanks Williams

I have JP drivers license, One more thing, I am planning to rent a car from Tachikawa stn, How much would be the toll?
Also if we do fruit picking eating in day time and later go around fuji five lake and be back to Tachikawa by around 9 PM would that be possible/rushed up?

We haven't driven in the Fuji Five Lakes area, so could not comment on the traffic situation there. As for the toll fee, you can do a search by using the following:
http://www.driveplaza.com/dp/SearchTop#search_map

A rough route search using Navitime reveals 1350 yen toll fee between Tachikawa and Kawaguchi-ko
http://www.navitime.co.jp/drive/