Some people do consider .7 adequate but I would prefer .8 or higher.
First, make sure all you items are coded in the same direction, because alpha assumes all the correlations are positive. Next, look at alpha "if item deleted" to see if any one item is dragging down you overall coefficient.
You did not say how amy items are in your scale, but if there are at least 6, then I would recommend doing an Exploratory Factor Analysis to see if you have more than one scale. For settings, you could use Principal Factors with an oblique rotation to allow for correlated factors.
0.679 is within the acceptable range. Nevertheless, if you still want to improve the value, you can try the following:
1. Identify outliers (extreme values) in the scale total and remove those responses.
2. If it is a self-developed scale, make a copy of your original data file and delete one of the items in the scale to see if it improves the Chornbach Alpha value.