I was just given a pair of Goodyear Wrangler RT/S 235 75 15 tires .  Would they fit on my 1993 Sidekick JLX 4 door 4X4?  They dont look much bigger than the 16's I'm running now, but I'm afraid they will rub.  Thanks for your help.

they will fit no problem, but you said you have 16 " wheels and will have to get differant wheels.

I ran my BFG 235's for nearly a year before I put the lift on. Slight rub on the plastic inner fender at full lock, & top of the wheelwell in the rear when flexed. Nothing bad enough I couldn't live with though. This was with 15x7 rims with a 4" backspace.

235/75R15 tires are commonly reported to fit the Sidekick without modification.  7" rims are a good choice for this tire size (it's what I'm using (on a Samurai)).  I bought mine locally for around $50 each.  For this tire width, OEM Suzuki wheels are really too narrow, but some guys run 'em anyway.  7" rims ordinarily have NO offset or special backspacing.  
Some good wheel info at:  http://www.rsracing.com/tech-wheel.html   especially the backspacing chart.