GA pilot reported the pilot flying flew into a box canyon resulting in a controlled flight toward terrain event. Flight cleared terrain and continued.

Narrative

During a pleasure flight with myself and the pilot flying; evasive action was taken to avoid controlled flight into terrain.On approach to land; I suggested to the pilot flying; that we should make right hand traffic for runway 07. The pilot flying opted to land straight-in for runway 25. I consented. After a low approach and a light touch-down of the main wheels it was determined to make a go-around. The pilot flying applied full power and executed the proper go-around procedures. Unfortunately; the aircraft did not perform as expected and the resulting rate of climb was poor. As the aircraft was flying into a box-canyon an immediate decision was made to execute an immediate right turn. The right turn resulted in flying into rising terrain and near buildings; but at a lesser gradient. Fortunately; the aircraft climbed just enough to clear the ridge of climbing terrain and the flight continued uneventfully.On reflection several Aeronautical Decision Making factors were lacking.1. The decision to land on the runway toward rising terrain did not take into account a go-around.2. Density altitude that day was high and was not considered.3. The comments in the chart supplement recommended that takeoffs be made on runway 07.4. Lack of fully briefing the landing at the applicable airport.In the future; these factors can be more fully addressed by taking time to consider all the potential outcomes of a rejected landing. This should be done by fully briefing the landing and rejected landing prior to choosing which runway to land on.