If this is the first PCB you have designed, this is really a good start!

But I would suggest few things:

1.  Try to arrange the component in such way that the track length is smaller. Example : In this design you can rotate the Arduino board 180 degree, so the track between the Arduino and the other components would be shorter.
2. Don’t keep the tracks very close to each other, check the manufacturers capabilities what should be the minimum distance.
3. Add copper pour to board, it reduces number of failure board produced during manufacturing.
4. PCB is always done to minimize the size of the component and decrease the cost of manufacturing. So if possible replace Arduino UNO with ATMEGA328P or atleast Arduino Nano/Pro Mini

You can read more about PCB design guidelines here and You can watch video tutorial about routing here.