Lychee Park is at the center of town and easily accessible from the Metro stop Da Ju Yuan. This Metro stop is the same one as MixC a big malI with everything in it and Carnival Spa (my favorite Spa in Shenzhen) I can't recall the exit but you can ask for "Lychee Yuan Lin" and people will direct you to the right exit.
The park covers what would be 15 square blocks in NYC. You can walk it all in about 4 hours with several photo ops. I did not see any food sellers inside so eat before going. There was a restaurant area but it looked run down and even closed when I went. Inside you will find several things of interest. Taichi classes, Older folks dancing along to lively Chinese pop music (Yuan10/month to join), a children's park with a merry go round, a mini pagoda used as an art exhibit area, lot's and lot's of couples in wedding garb taking photos (on weekends), bridges and footpaths. There is a bee farm that also sells honey. Everyone is local. This is a snapshot of local Shenzhen. The signs are bilingual though so you can sort of get a sense of where you are and whole park maps are around but in Chinese only. Just like in Central Park you have the skyscrapers looming never far away. At the corner exit (near to Mix C) there is a HUGE poster of Deng Xiao Ping the former leader of the communist party and the fellow who decided to give Shenzhen its Special Economic Zone status enabling it to boom. This reverence to him is real and you can't help to enjoy the locals taking photos next to their hero.