Question

Where does the capturing of light energy in eukaryotic cells mostly occur?

Answer 1

In eukaryotes absorption of light energy and its conversion to chemical energy most probably occurs in the thylakoid membrane of chloroplasts where the green pigment chlorophyll is embedded.

Thylakoid membrane constitute small flattened vesicles,the thylakoids which are commonly arranged in stacks termed 'grana'.The space inside the thylakoid disc called thylakoid space or lumen.'Stroma' is the fluid surrounding the thylakoid(where the carbohydrate synthesis occurs).
The membrane contains many integral proteins to which light harvesting complexes are bound (notably chlorophyll).

Chloroplasts are unique organelles captures light energy from sun to produce free energy stored as ATP and NADPH,through a process called photosynthesis.