Few things you can do, like Google "location of strawberry farms near Beijing" for more results.

One of the largest strawberry growers near Beijing is located at 2001-1-1, Nanxiaojie, Guangqumen, Chongwen District, Beijing.  They have about 800 greenhouses full of strawberries for you to pick.

Or visit
http://www.btmbeijing.com/contents/en/btm/2010-04/feature/pickingcalendarfreshnessathand
for further information in English

There are lots of places in the suburbs where you can go picking strawberries.

There's a place in Shunyi called "北京绿富农果蔬产销专业合作社" which offers public strawberry picking until June. Their strawberries are quite expensive however - 60-150 per 500 grams.

地址：顺义区木林镇贾山村南100米
Tel: 13911537404 010-60459195

Cheaper places can be found in Pinggu, Fangshan, Changping and Daxing Districts. If you can read Chinese, this website has all the details:
http://strawberry.likefar.com/

There's a place in Shunyi called "北京绿富农果蔬产销专业合作社" which offers public strawberry picking until June. Their strawberries are quite expensive however - 60-150 per 500 grams.-Redaria

I can agree with Redaria. Strawberries and berries are more expensive in China. 

If you do go strawberry picking it won't be free. And it won't be without someone constantly watching you. Nothing is free and that is also true about picking strawberries in China. Somebody owns those strawberries so most likely you can't just go picking strawberries in a field. 

You won't be able to find any places in the inner city but on the outskirts of china places like the far North West of Beijing offers places to pick strawberries.