I can recommend http://unity3d.com/. Very easy to use, powerful and you can become productive quickly. It has support for multiple platforms, including iOS/Android. I believe you can make games for those platforms even with the free license (although under restrictions).
I'm not sure if you can access the accelerometer directly from their engine, but I'm certain they allow you to write wrappers to access the underlying OS features. I know a project where we had our native cross-platform library which we could load independently of the platform used through the same C# wrapper code in Unity and through it we could directly use android/iOS library.
If I was an indie just wanted to create a game that would be my engine of choice any day of the week.