We present calculations of various properties of the ground and excited states of Coumarins 151 and 120. These and related coumarins are important in investigating ultrafast solvation processes in liquids and complex solutions as well as being important acceptors in model electron-transfer systems. We calculate the following: (1) the electronic excitation energies to several low-lying singlet states, (2) ground and excited-state dipole moments, (3) solvation effects on excitation energies, and (4) the properties of single Coumarin 151-water complexes. We test our Time-Dependent Density Functional Theory (TDDFT) calculations against CASSCF, CASPT2 (both single and multistate versions), CIS, and ZINDO. Using TDDFT, we find excellent agreement with experimental S-1 --> S-0 excitation energies. On the basis of these results, we address several outstanding questions for these systems and find: (1) that TICT-formation is unlikely upon photexcitation for gas-phase C151, (2) a greater tendency toward a planar amine group for the S-1 state than for the ground state, (3) significant differences between our gas-phase ground-state dipole moment and the experimental value, and (4) TDDFT results for water-Coumarin 151 complexes are in good agreement with the experimental results of Topp and co-workers.