There's a fantastic view of Pyatigorsk, and all the way to Mt Elbrus on good weather days, from the 993m summit of Mt Mashuk. You can reach here either by hiking up a tree-shaded road or – easier – riding the cable car. The best views of Elbrus are early in the morning but it's also a lovely spot to come to for sunset.
If you’re hoofing it, Mt Mashuk is about a 45-minute climb from the cable-car station. You can also rent bicycles next to the lower cable-car station.