Though I'm not sure that I'd recommend it (sales presssure), Westgate Palace is probably the closest to Universal - about 2 1/2 miles.
There are others: Westgate Lakes about 4 miles, Marriott's Harbour Lake and Marriott's Cypress Harbour (across the street from one another) about 6 miles, etc.
I agree with Brian Noble that the facilities at Harbour Lake at excellent for younger children. But Cypress Harbour's facilities aren't bad either.
Dick Taylor