Rest areas, Walmart, truck stops. All 3 will usually do, and each has their caveats.
Rest areas usually fill up late day with big rigs, and if you do find an empty lane, the noise and smell might be problematic. Haven't had any safety issues at them. Doesn't mean it can't happen, just nothing so far.
Truck stops are OK, but few have lots of RV parking, and it's usually not a good idea to use "truck parking" areas to overnight. During the day when they're less full, maybe just for short periods. We've asked at a few Pilot/Flying J locations and the manager said go ahead and park there, because it was marked Truck/RV parking. If it's marked Trucks or Trucks Only, avoid.
Walmart is a funny animal. It's usually OK, if you're not the only overnighter, but you can always run into problems. We've had a couple of scares over 10 years of stopping at Walmarts for the night, and you just have to be aware of your surroundings in them. We try to avoid anything close to the center of a city. Better to stay at the ones just off the interstates, or near the outside edges of town. Even that can be dicey, though.
Gary's suggestions are also good ones.