Hi LuvSnowWhite, welcome to MouseBuzz!
I hope you love it here!!
I don't think the Universal hotels offer transportation from the airport (they need to get on that bandwagon ASAP if they want to compete with Disney!) but I would second Cincy's suggestion to use Quicksilver! Very affordable, convenient towncar transportation is such a blessing when you just want to get to your hotel and relax after traveling.
I am jealous of your combo trip - I have always wanted to do that! And I definitely think you're doing it right...Universal first, saving the best (Disney of course
) for last!