Where to see big cactus in AZ and/or NM?

They are only in AZ. You can start to see them on I17, past Sunset Point, as you descend into the Valley. there are a lot to see there. If you are coming from FL, consider coming on I10 and then go up to Utah via I17. You will see a lot and do not have to go to the National Park to see them. Then you can get to Southern Utah via the Grand Canyon, Monument Valley, etc.

I don't recall seeing any in New Mexico but from Phoenix to Tucson you'll see many. They are awesome, especially in bloom - usually April/May depending on the weather. To really appreciate them you need to walk amidst them. Saguaro Nat'l park east and west have nice trails. Catalina State Park at Tucson is a nice place to stay. In the Phoenix area, stay at one of the Maricopa County Park campgrounds (electric) which have huge sites landscaped by nature with the saguaro and other types of lovely cactus. Lost Dutchman State Park at Apache Junction is another excellent place to stay and some sites have full hookups.

Summer isn't the best place to tour these cities though. It's HOT!!! It starts getting hot and dry in May and quite often in March and April but Feb-April are prime wildflower/cactus blooming times.

You won't see any Saguaro cactus until you get into the lower desert regions of AZ. Pretty much from Phoenix south is where you'll see them.

Tuscon has two National Parks called Saguaro ------ tells you something about them being in the area! I do not know how much further north to Phoenix area they go and certainly not at altitude. There are a bunch at Picacho Peak near Casa Grand and also west on I8.

They are only in the Sonoran Desert which you can find on a map. Less than 30 miles north of Phoenix they are gone.
RichH

Pick the right road and they are there by the thousands.

SR89 north of Phoenix for instance. And just outside Tucson on the back road from Florance. US93 has lots of cacti, also.