The east facing side has almost ideal planting conditions. It has mostly morning sun which is very kind. The area probably closest to the house would be the place I'd put the plants that don't like afternoon sun (since they might not get the 1 pm to 2 pm sun and would be spared). This would be azaleas and hydrangeas - they love morning sun but don't like the hot afternoon.

The west facing side would need to be plants that can take hot afternoon sun, however they only get about 4-5 hours of sun total which is not always enough for plants that need full sun (6 hours) to bloom well.

I would put the morning glory on the east side, further away from the house as it can handle the most amount of sun.

Hope that helps.