If you're looking for somewhere to go for a walk, Roundhay Park is beautiful, however it is very popular and the car parks and roads around get very busy, so parking can be a little tight. We have been several times and although the paths around are solid under foot, they can get very muddy, so in the winter months, you may want to think about your footwear choice.
The map below shows one of the longer walks we have done around the lakes at Roundhay Park