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there are numerous places where you can take off the main Forest Road for a camp spot - excellent views are from the top of Humboldt Peak (sign to the right when coming from Scottsdale, most of the incline is paved asphalt)
there are also numerous possibilities for camping right off Four Peaks Road, on the valley side as well as on the Roosevelt lake side - totally doable in a Subie - prime look-out spot would be the large cleared area just right up from the end of the dirt trail to Lone Pine Trailhead
going down FR401 to Sycamore Creek and up a bit FR1852 towards Ironwood Ridge would also get you to camping spots that are not crowded
I think I would prefer places off of FR403 down from the Sugarloaf exit off Beeline, even before you get all the way down to what is known as Sheep Camp and is the crossing of upper Sycamore Creek - plus, there are very nice spots the deeper you get into upper Sycamore Creek along FR1855 - but depends on water level in the creek
further up Beeline, going right at the intersection with Mesquite Creek will get you into a broad creek valley, although the scars from the big Bush Fire in 2020 are still evident; plenty of camping opportunities around there - to the left will get you into an area that easy to access in a Subie with multiple suitable camping spots, but also quite popular = crowded on weekends, probably
the Bushnell Tanks turnoff will not get a Subie very deep into the desert, but usually it's not crowded, either
up the road to Mt. Ord is another possibility, although getting colder these days at that altitude
oldie-goldie: go into Bulldog Canyon from the south (better for a Subie) or the Usery entry area (more scenic) and find many suitable camp spots - you need a permit, which can be pulled online:
Tonto National Forest - Bulldog Canyon Off-Highway Vehicle Area - https://www.fs.usda.gov/recarea/tonto/recarea/?recid=35555 via recreation.gov
