  The purpose of this paper is twofold. Firstly, we prove transportation
inequalities ${\bf T_2}(C)$ on the space of continuous paths with respect to
the uniform metric for the law of the solution to a class of non-linear
monotone stochastic partial differential equations (SPDEs) driven by the Wiener
noise. Furthermore, we also establish the ${\bf T_1}(C)$ property for such
SPDEs but with merely locally monotone coefficients, including the stochastic
Burgers type equation and stochastic $2$-D Navier-Stokes equation.
