There is also this long review paper"Review of Geometry and Analysis" by S.-T. Yau from(Asian Journal of Mathematics, vol. 4, no. 1, pp. 235-278, March 2000:
http://www.intlpress.com/AJM/p/2000/4_1/AJM-4-1-235-278.pdf
), where he discusses many big open problems in Riemannian geometry, symplectic geometry, algebraic geometry, and geometric analysis. This can keep you occupied for a long long time...