Try pulling up each of your three segments on ITA, one at a time, forcing the connection in CHI, and sort by Duration. E.g., [from] "NYC:: CHI" and [to] "SAN".

NYC-SAN: you can book overnight layovers in CHI out of any of the NYC airports, using AA/DL/US/UA as appropriate. Then standby for the first flight out in the morning for NYC-CHI and you can get about 24 hrs in CHI. This is Mrp Alert's advice and probably your best bet.

SAN-CHI-ORL looks harder due to timezones. Could book redeye and standby for daytime flight, but probably doesn't get you as much time in CHI. ORL-CHI-NYC also looks less attractive.

(Note that a lot of the itins ITA will show you are actually two segments fared separately. Not necessarily bad - you may discover that, since some of these fares are quite competitive, if you're flexible you can book four separate segments and get as much time in CHI as you like without worrying about connection times.)