Negative vibes on here about Arizona and the FAA which I cannot agree with. I've landed at most airports in Az (except PHX) and found the reception always helpful and sometimes, as at Lake Havasu for instance, overwhelming.
Flying in the US is far less stressful than here. However I do think your 50Hrs in 2 weeks is pretty optimistic. Something like 2Hrs per day will be much more comfortable though I appreciate you probably have a 3Hr minimum from the FBO.
Above all else, fly early. Everything's open by 6am and the air is much calmer than in the afternoon. I find it also helps no end with jet lag if you stay closer to UK time.
Your FBO checkout will undoubtedly cover getting into or under the PHX class 'B'. However you might also consider having the instructor accompany you on a cross country to an uncontrolled field like Payson (very pretty). US instructors usually don't appreciate the differences between UK and US training and may not realise that you are not familiar with the 45 deg join, just as an example.
Don't be put off by the partly justified reputation of certain fields like Sedona or the Canyon airport. Compared with the 600m grass strips we are used to here, they are a pussycat, downdrafts n' all. Do check the FBO's policy on where you can land though since some do ban Sedona. Also be wary of gravel strips like Temple Bar, even if allowed by the FBO, because it's easy to pick up stones.
Interesting places (I've mentioned a few already) include Valle with it's museum, St Johns with the white mountains, little unnatended Winslow (with the crater and picture of Lindburgh in the hut that serves as a terminal) and Bullhead City with the Nevada casinos right across the bridge. And there's Deming and Bisbee (with mine tours) right down on the border if you want to see, but not enter, Mexico.
Provided you are light (max +1 in a typical 172) the Canyon VFR routes are eminently achievable and the memories will last a lifetime. Route N across the Canyon to lovely Page, Az., and be sure to get a room in the Best Western overlooking the river where they filmed 'Evolution'. From Page go E to Monument Valley and then S to the San Fransisco Mtns and Sunset Crater before landing at Flagstaff, where you can visit the famous observatory (check for opening times). I've met pilots (In Prescott) who claim they've never flown outside of Arizona. Once you are there, you will see why.
Hope that helps.