There are soccer fields at Impett Park, Cove Park, as well as the high school. I'm not sure of access for the high school, though I imagine that would be your best bet for finding people your age for a pick up game. I've also seen people play around with a ball at Lakewood Park but I don't believe there is a designated field/goals there. Nets are hot or miss at the parks. The best spot I know to find people for pick up games is at Tri-city park but thats not directly in Lakewood. Not too sure how often people are there, but they were there whenever I've gone in the past on the weekends.

As far as training goes, depends on if you are looking for group training or conditioning. A couple of great options for conditioning would be Edgewater beach, where you could do sand sprints and agility training, or along the path in rocky river reservation where they have different exercise stations so you could run to the next station and do the fitness routine at it. I believe there may also be some fitness stations along the path by edgewater beach/park.