I took this picture looking toward Sin-el-Fil from Sioufi Garden, the public park that my kids like so much.
If you want to visit the Sioufi Garden you might find this map helpful. The park is south of Achrafieh, marked by the red oval and the red arrow shows where the entrance is. You can get to the park lots of different ways, and I've tried to indicate where the major roads in the map will take you.
The garden seems to be open from sun up to sun down, no entrance fee since it's a public park. There are a couple pools of water, ideal habitats for tadpoles and minnows and geese. Sioufi Garden also features many sculptures. Visitors to the park are free to touch and climb on these pieces of art. There are lots of benches throughout the park and a lot of play equipment (slides, swings, etc.) but it isn't all in good repair, so you've been warned.
This park isn't ideal for biking--paths are uneven. The whole park is situated on a hillside, so only really small-scale ball-play would be workable.