Solly,
The Livermore suggestion is a bit out in the sticks, so it's definitely rural.
Del Valle is a regional park (also designated a state recreation area), approx 7 miles from town and 6 miles from anything. We've stayed there a few times, but that was in the 80's (1980's that is). There's a nice lake in the park and, if you're into fishing or boating, you can rent a boat and explore the lake. Summer time there are a couple of beaches for swimming. There are also great walking/nature trails. If you're into wine, Livermore has 25+ wineries and you'd pass some of them en route to Del Valle.
When we first moved to
Livermore in 1990 it was what I called a 1-horse town, with nothing to speak of on the main street apart from my barber who'd been there 30 years, a western wear store, a saloon and a bar & grill. The town has changed significantly over the last 10 years and you now find a few decent restaurants, including a couple of Italian places. The bar & grill is still there and has a live group on weekends. But you really should wear your cowboy hat and boots to fit in with the locals. Some of the wineries have good restaurants, by far the best being the one at Wente Brothers winery, just around the corner from our prior home.
With advance notice, you could tour the Lawrence Livermore National Laboratory on the outskirts of town and not far from where you'd turn towards Del Valle. But they require a couple of weeks notice for foreign nationals.
If you were there in June, Livermore hosts an annual rodeo, quite an event if you haven't seen one live.
A little trivia for you ... the town of Livermore is named after Robert Livermore, an Englishman. You can read more about it
here.