I ferried a Chipmunk from Ontario to Los Angeles a few summers ago. It took about 4 days (perhaps 5?) and that included two half-days down due to weather/maintenance. The Chipmunk is obviously a lot slower than a C172 (I think we averaged about 70 miles or so per hour!) and we flew at least 3 legs a day with only time for supper and a quick breakfast at each stop. I don't remember what we did for lunches, but probably granola bars/FBO snacks, etc.
I'd completed all the planning -- using paper maps (and downloaded digital airport facility directories on my phone... this was before I had an iPad and a ForeFlight subscription!) -- before we left and the trip went almost exactly as planned. Pretty exhausted by the end, but some fabulous open-cockpit flying, great views, met some amazing people, and got to re-visit folks/FBOs from previous flying jobs in the US.
As a caveat - at the time I was working as an aerial survey pilot which had me flying from job site to job site and had tons of ferry-style flying under my belt, quite a bit of it in the US. I had several thousand hours by then, and I knew my personal limits, how to be super efficient at each stop (an hour max, usually less was planned) and exactly how flight planning and stuff like that worked. All this being in turbine machines.
The aircraft added a special element to it, obviously, because it being quite vintage with a big old iron engine and flying in the heat of the summer, I needed to plan for appropriate oil at the stops (the owner was running it on Mineral), worst case scenarios (i.e. route planning based on an engine failure any time!), and the limited performance, climb/speed, etc. There was no way in hell I'd be crossing the mountains at SLC and BOI like during previous trips in better performing a/c! so I went all the way around via El Paso. (Loved TX, BTW, if you get a chance to stop in Pecos, it's a fabulous overnight with a lovely FBO and owners.) I'd also planned hangarage at each overnight, but that may not be practical for you. (I had the advantage of the new owner of the aircraft being quite well off - he was able to pay for this to ensure his new "baby" didn't get damaged on the trip
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The awesome thing about flying in the US is once you land at the FBO, they have special rates at hotels and usually courtesy vehicles - or someone will drop you off at the very least. They love General Aviation down there, and you will likely find you're very welcomed, as opposed to Canadian airports where you're often left to your own resources.
I'll send you a pm with a link to the trip log - maybe you'll get some inspiration and insight.
Good luck with planning!