  We use microlocal and paradifferential techniques to obtain $L^8$ norm bounds
for spectral clusters associated to elliptic second order operators on
two-dimensional manifolds with boundary. The result leads to optimal $L^q$
bounds, in the range $2\le q\le\infty$, for $L^2$-normalized spectral clusters
on bounded domains in the plane and, more generally, for two-dimensional
compact manifolds with boundary. We also establish new sharp $L^q$ estimates in
higher dimensions for a range of exponents $\bar{q}_n\le q\le \infty$.
