It's very windy in Rodeo, so fasten all your stuff and always put something heavy on your hitchhiking sign when you put it down. Let's not pollute the place.
South towards Las Flores border crossing, Barreal
From the plaza in Rodeo, it's a 4 km hike uphill to where the town ends and the Rodeo bypass meets the town's central road. The town thins out before that happens though, so there's a good chance of catching a ride while hitch-walking out. At the crossing, you can put up your thumb and catch a ride to Pismanta or Las Flores. In Las Flores you can go to Chile via the Paso Agua Negra border crossing, which is open only part of the year. In summer, there's many people staying in Rodeo before hopping over to La Serena in Chile, so it might be worth it to ask for a direct ride across with some people. Mind of a Hitchhiker got offered a ride by a friendly Argentinian couple in January 2017. Otherwise, head for the YPF gas station in Las Flores. Nearly all traffic will stock up on fuel at this particular gas station before making the crossing at 4.780 meters above sea level.
If you're going to Barreal or taking the adventurous road to San Juan city, ask for rides directly to Iglesia, the last town before the spectacular RN 149 leads to nowhere in particular.
Stand on the Ruta 150 out of town, close to the lake. There's nothing between Rodeo and Jachal. San Juan city should have quite a pull from Jachal, as it is the popular route.
Accommodation and Sleep
Only the strongest of tents can withstand the wind power here. Pitch it in the wind shadow behind a wall or building, or hide in one of the hostels. You can camp "inside" some hostels for half price and make use of their amenities if you can afford a middle-ground solution.
Other useful info
Windsurfing and kitesurfing is big here. You can rent gear or take classes if you have the cash. From the town center to the lake is a 6 km hike. They have one ATM there and a few places with spotty WiFi and doubtful electricity, too. At the lake shore is as of January 2017 no telephone signal (neither for mobile internet, nor for calling/texting folks).