Inspiration can come from literally anywhere - so it's always best to keep an open mind. If you try too hard to focus your energies on gaining inspiration, it may never come. If you leave your mind's door un-latched and get on with other things, you'll be surprised at how many ideas can flood into your subconscious mind.
One of my favourite ways to gain writing inspiration is to take a drive out into the countryside and gaze at all of the wide expanses of fields - it's amazing how landscape of any hue can actually stimulate the imagination and let it run around a now free and un-clogged mind.
Another way to open yourself to inspiration, is to invent 20 names that you particularly like the look and sound of and then write a couple of lines of back-story for each. You can invent some really absurd names if you are writing a children's book or satirical work, i.e. Sir Gerald Higgenbottom-Cleesthorpe or Jeremiah Uttsworth the Third - and then really go to town on what you think they have been up to in their lives.
You'll find one or two of those imaginary people really spark off a chain of thought that leads you to where you are going with your writing project. Even if you go on to change their name, you'll find that you cannot stop writing about them once you have started.
Another source for inspiration are your dreams. Sir Paul McCartney wrote Let It be after having a dream and Mary Shelley had the idea for Frankenstein after dreaming about that ground-breaking entry into the pantheon of monsters. You could start by buying a notebook or actual Dream Diary and make notes on your dreams when those dreams are fresh in your mind, the moment that you wake up.
What I find is that creativity breeds creativity - so once you've opened up to the possibilities that your imagination can give you - inspiration will never be far away.