I just bought a 4'' skyjacker suspention lift and i am wondering what size tires i can put under it? height and width... i have bought new wheels with the offset at 3.75. stock is 4.75 so they stick out 1 ''... i dont know if that helps    

I currently have a 3.5 in lift and fit some 33x13.5's mounted on 15" rims on mine with about 1.5 in of clearance in the wheel wells. I know you said you just got new rims, but you can get 4 supper swampers mounted on powder-coated rims with lugs and center caps from desert rat for about 900 with a lifetime warranty. Dont know the backspacing, but i get verry little rub at full turn.  

would 34x10.5 fit good on my 15x8 rims with the 4" lift?  

I would say probably.. almost definately. But the best people to ask would be the people you want to buy the tires from or a place that deals with the lift you bought (ex. quadratec)  

i have 33x12.5 on a 3in lift, if you go much bigger that 34's you may need new gears