An excellent hike near Villa Belgrano is to Cerro de la Virgen, a peak which overlooks the town, to which there is a fairly well marked path from the main road.
From the centre of town you take Avenida Ojo de Agua as far as Ruta 5, then take a right until you see the clearly marked entrance to the hike on the left-side of the road. It's a straightforward, though steep climb to the summit. The summit is marked by a small shrine and a placard naming the peak. There are excellent views of Villa Belgrano, the surrounding region, including Los Molinos lake, and, on a clear day, to Cerro Champaqui, the highest peak in Cordoba province (2790 m), in the west.
I´m not sure of the altitude of Cerro de la Virgen, but it's over 1000m, and it takes about 45 minutes to hike to the top.
If you've reached the summit of Cerro de la Virgen (see my previous tip), a slightly higher mountain, Pico Aleman, is within easy reach. Follow the path upwards from Cerro de la Virgen and after about 10 minutes you'll arrive at Pico Aleman summit, marked by a sign, from where there are even better views over the town of Villa General Belgrano and the surrounding region. The path to Pico Aleman from Cerro de la Virgen is easy to see, but take care as there are some prickly bushes along the way.
Arroyo el Lomo and Arroyo el Sauce pass through Villa Belgrano, and the banks of these rivers are nice places to relax and escape the heat, or perhaps to have a picnic. There are paths running along the banks of both rivers and it's easy to find your way alongside them. I recommend you pick up a map from the tourist office showing the routes.
Villa Belgrano's modern tower, completed for the 2002 Octoberfest, can be climbed, and offers a good view of the town and the surrounding area, especially of the the mountains Cerro de la Virgen and Pico Aleman, to the east. The entrance is in the tourist office, it costs 1 peso and there are 98 steps leading to a lookout room, with windows in all directions. You also get a close up of the Senora & Senorita statues in the building next door: when air pressure is low, Senor is more prominent, and when it's high, vice-versa.