Tbilisi summers are hot, so finding a watering hole and somewhere to get down to the swimsuits is essential, especially if you can't get over to Batumi. Turtle Lake (or Kus Tba in Georgia, which is how taxi drivers know it) is one of the closest and best places for this.
Being just up Vake Park, it's relatively easy to get to and it's quick. There's also a place to have lunch and drinks up there as well. And swimming - though the best watering holes are a hotly debated topic here.
It's a steep incline to get there, so just take a taxi.