Kensington Gardens is one of the royal gardens, which actually extends the Hyde Park area. The gardens are located to the west of Hyde Park, only separated by a road.
Kensington Gardens are a well kept and pleasant place to visit, as are all the parks in Central London. You can also rent deck chairs between March and October, if the weather allows it. The chairs cost £1.80 for the first hour and £9 for the whole day. You can also rent bikes, which you can only ride on bike routes around the gardens.
Also the Diana Memorial Playground is located in the park, where children under 12 can play in, amongst other things, a wooden pirate ship.
The nearest underground stations are Queensway (Central) and Notting Hill Gate (Central, District, Circle), roughly a 10 minute walk away.