Two good summertime meteor showers are the Delta Aquarids (active from July 15 – August 15) and the Perseids (active from July 23 – August 22).
Although they overlap, their peaks are about two weeks apart, on July 28 and August 12, respectively. However, this means the two showers peak during opposite halves of the Moon's phase cycle and take place under conditions that are reversed from one another—the Delta Aquarids only a day after a bright full Moon and the Perseids a day after a new Moon. So as far as picking one to watch, it's one or the other. Barring inclement weather, the Perseids are this year's pick, especially if viewing can be done away from city lights. Caused by Earth's passage through the dust trail of Comet 109P/Swift-Tuttle, the Perseids usually produce up to 80 very swift meteors per hour as seen from sites away from city lights, peaking on the night of the 12th and extending through the predawn hours of the 13th, ideally during the hours between midnight and dawn.
However, don't limit your observing to just the night of the peak. According to the authoritative MeteorShowersOnline.com, "It is possible to spot five Perseids per hour at the beginning of August and perhaps 15 per hour by August 10. The Perseids rapidly increase to a peak of 50-80 meteors per hour by the night of August 12/13 and then rapidly decline to about 10 per hour by August 15." However, these estimates assume ideal circumstances and should be weighed against local observing conditions. From light-polluted urban areas such as San Francisco, for example, the number of visible meteors forecast is about 33 per hour at the shower's peak.