The above little maps will give you a general idea about what is possible, but you really want to get a copy of the Green Trails "Saguaro" map.
Although it is certainly possible to visit the high country via long day hikes, visits to this area are generally best done via overnight backpack trips. Oddly enough, backcountry camping is restricted to 6 definite locations, and you will want to read the wilderness guide (also from the park website). You probably should check the official website for a copy in case they make changes to the regulations.
At this time (2010) the six spots where camping is allowed (for a fee of $6.00 per night, a backcounry camping permit is required) are as follows:
All are near a potential water source, which depending on weather and time of year
may or may not be a viable source of water.
You can call the visitor center at (520) 733-5153 to find out what they know about
the current status of water sources.
Tom's hiking pages / tom@mmto.org