30-40 miles will get you across the Sawtooth range in most directions. The Stanley, or north side of the range is the most visited and scenic. The Stanley side is also closer to lakes that offer decent fishing and if the runs weren't so low, we'd have a Chinook salmon season on the main river again this year. Redfish Lake is a great starting point and you can jump start your trip by taking the shuttle boat across the lake. Once you get in a few miles you might be surprised at how few people you see. Some areas in the inner range see few, if any visits per season. It's a low snow year and the range and trails are pretty much snow free now. There are many loops a solo person could do from the Stanley side that don't leave you stuck somewhere remote like the southern or western side of the range.
I was in the Rubies a few times and it's a beautiful range but the area we were in (Ruby Pass, Ruby Lake) was heavily used. The fire pits all looked liked they had a thousand whiskey bottles smashed into them and the trails were beaten by a lot of horse traffic. I never bothered to go back.