Dilemma in Landscaping: Narrow Side Yards

I believe I have dreamt up, chopped down and rebuilt ideas for every inch of this house now. Of course, none of these ideas are complete yet. But I realized that I'm still unsure about landscaping around the house. We have a nice sized backyard but I'm clueless about what to do with it. Hubby gave me a hammock for our anniversary so my ideas will be revolving around a relaxing retreat.

The biggest challenge will be the side yard that runs along our house and the icky chain link fence of our neighbor's yard (who chooses not to mow her lawn).

Here are some inspiring images I ran through today.