There is a great place to bivy below the Spires and Rexford on the west side. But it might be snow-free (hence no water) by now.
However, there's still snow at the top of the E and Ne ridges of Rexford. You can get water from there.
In general I would not recommend the Centre Creek approach to Illusions right now.
I suggest the following: hike up the Rexford trail from Nesakwatch right now.
Camp at the typical west side Rexford location. Flat bivi rock.
Do the Illusions traverse one day, return to camp. See TR here:
http://www.clubtread.com/sforum/topic.asp?TOPIC_ID=57444
Then do the normal North Spire-South Spire-Rexford traverse the next day (plenty of TRs including a fewfrom this year available online), and hike out down the Rexford trail again.