There are several locations where you can find money to buy hats at Weathers, the hat store, in Goat Bay City.
There are ten locations (That I know of) for the money. The easiest way to do this is to grab the money from the restaurant (Numbers 5-8 below) and the two in the Put-in Hotel (3-4).
1: Immediately from spawn, walk down the street and on the back side of the big blue house, there is a gravel path. Walk onto it and into the white house. Go up the stairs and to the right into the green room. The money is located on the dresser in between the beds.
The rest are in close proximity to Weathers.
2: There is a stack behind the front desk of the hotel. It is on a smaller desk against the back wall with a monitor and speakers.
3-4: There are two more in the upstairs area in the lobby of the hotel. Run up the stairs and all the way to end of the right to find a row of backless chairs against the wall.
5-8: Looking towards Weathers and the other shop from the front of the hotel, turn right and head to the small path beside the yellow building (along the left side of the river). From here, walk towards a restaurant area and there will be four stacks of money on the tables.
9: Another stack in behind the convenience store beside Weathers. The stack is on the checkout area.
10: At the club near the back of the hotel, there is a stack on the large desk at the back of the room.
11: There's some money under the lift up to the rollercoaster - you can grab it from underneath when it raises up (Thanks to Bridge88).
12-13: There's also two in the drug house ("Magic sugar") - one in the same room as the sugar, and one in the bedroom where the guy is using the computer, on a bookshelf (Thanks to Bridge88 again).
Once you have the money, head back to Weathers and give it to the clerk.
If you know of anymore, let me know and I'll add it to the solution and give you credit