Many trees actually repel bugs, such as the cedar tree. You can probably do a search of the tree you plan on cutting down, and see how it works as mulch . The chips from just about any tree should be awesome for making any kind of paths through the garden, or even through your yard, of you want a path somewhere. Another possibility, is around shrubs, like azaleas, or rose bushes, to keep the weeds from coming up around the base of the shrub.