POSTGRESQL: Using case with joined tables

I'm a Postgresql newbie, so still struggling a little bit here. Please be gentle.

I'm left joining three tables, and would like to be able to use a case statement to introduce another column that brings across a desired value from one column based on another. I'm going to guess that my INNER JOIN and CASE statements are back to front, but I'm not sure how to rearrange them without breaking the intent.

Basically: Where model_best_fit == SUNNY, then I'd like a new column with name applied_f_model_hours_above4k to have the value from the column hoursabove4k_sunny

Code sample:

SELECT *
    FROM px_fuel_weathercell
        INNER JOIN f_descriptions ON px_f_weathercell.px_id = f_descriptions.fuel_id
        INNER JOIN dailywx ON px_f_weathercell.fid_new_wx_cells = dailywx.location
        CASE best_model_fit
            WHEN 'SUNNY' then hoursabove4k_sunny
        END applied_f_model_hours_above4k
    WHERE best_model_fit = 'SUNNY' /* limiting my test case here, clause will be removed later */
LIMIT 1000; 

The error is as follows:

ERROR:  syntax error at or near "CASE"
LINE 5:   CASE best_model_fit
          ^
SQL state: 42601
Character: 210

Thank you for any help you can offer.

Bonus points: CASE seems slow. 45 seconds to run this query. dailywx has 400,000 rows, px_f_weathercell has 6,000,000 rows. Is there a faster way to do this?

EDIT: Made the following edit, no getting a column full of nulls when the column desired has numbers (including 0) in it. Both columns are of type double.

EDIT2: Updated a couple of table names to indicate where columns are coming from. Also updated to show left join. I've also used PGTune to set some recommended settings in order to address a situation where the process was disk bound. I've also set an index on px_f_weathercell.fid_new_wx_cells and px_f_weathercell.px_id. This has resulted in 100,000 records returning in approx 5-7 seconds. I'm still recieving null values from the CASE statement, however.

SELECT *,
    CASE best_model_fit
        WHEN 'SUNNY' then dailywx.hoursabove4k_sunny
    END applied_f_model_hours_above4k
    FROM px_fuel_weathercell
        LEFT JOIN f_descriptions ON px_f_weathercell.px_id = f_descriptions.fuel_id
        LEFT JOIN dailywx ON px_f_weathercell.fid_new_wx_cells = dailywx.location
    WHERE fuel_descriptions.best_model_fit = 'SUNNY' /* limiting my test case here, clause will be removed later */
LIMIT 1000;