If you have one or two drinks at a weekly happy hour, you probably have minimal negative – and possibly a positive – effect on your overall health. Likewise, this amount of alcohol probably does not adversely affect your training run performance. Alcohol can have a mild diuretic effect on your kidneys, but if you are eating a normal diet with accompanying fluids, you will not likely have problems with your hydration.
If you are competing the next morning, I would shy away from any alcohol, especially if it will be hot. This comes from my experiences at the Falmouth Road Race where we would usually care for 10 to 15 runners with exertional heat stroke each race, and one thing several of the affected runners had in common was alcohol ingestion the day prior to the race. While not universal, it did seem to be a risk factor for developing heat stroke. Alcohol also acutely increases risk to athletes in the cold, but that increase in risk is more related to acute use rather than ingestion from the prior evening.
If your happy hour drinking habits tend toward the excess side, you are probably at more risk from adverse effects of alcohol. Alcohol may negatively affect muscle energy metabolism, which would reduce performance and increase perceived effort during the run. Larger doses will affect both strength and power, and may reduce your overall endurance. If you go into exercise depleted (dehydrated) from drinking alcohol to excess, you raise your risk of heat stroke and reduce your performance times; and if you go into your running session cognitively impaired, your risk of injury will likely be increased.