Chandler Aviation seemed quite reasonable when I was there but I understood that hours building was conducted with a CFI sat in the R/H seat for the entire time for insurance reasons which seemed to defeat the purpose of hours building to me. Perhaps this has changed now - it was a long time ago. You will be pleased to discover that you seldom pay for landing/touch & go's in the U.S. You may pick up the odd 'handling' charge if you plan to visit larger, busier fields like Las Vegas McCarran for example. Conversely, never paid anything for movements at PHX, TUC, OAK or SAN.
If you are obtaining an FAA Private on the basis of a Foreign certificate you will require an FAA Flight Review which you should be able to combine with a school checkout if you discuss with the instructor beforehand.
Arizona is a great place to fly this time of year with close proximity to CA/NM/NV although a few hours away in a 152 to reach the West Coast with not much inbetween . The best advice I would give is keep your eyes open - extremely busy airspace around Phoenix with numerous flight training organisations and many student pilots plus a more diverse range of traffic than you usually see VFR in Europe.
Alternatives could be Florida - again, nice this time of year but a bit limited with respect to 80 hours of meaningful navex's; California is good although taxes are higher and weather not as predictable as the two already mentioned. Utah and New Mexico offer good alternatives for both weather and financial incentive.
If you are planning to do it soon, I presume you understand that unless a US citizen, there is a requirement for TSA approval to undertake instruction?