A Present for Piglet

First, you solve the puzzles:

An Area With Big Stones and Rocks MONTERA
A Pile of Blocks PARTY
Audio/Visual Equipment Closet CHESTNUT
Denver Botanical Garden LEMON
Hall of Justice FOREST
In the Park BLUE
On The Runway COCKTAIL
The Islands of the Cartesian Sea PIRATE
The Sixth Floor Games Lounge MAGENTA


Then, each of the puzzle answers has an answer which is either a color or a hat. Gathering the answers by type, you'll notice that the answer lengths are all distinct, which gives an ordering for each type:

A Pile of Blocks PARTY (hat, length 5)
The Islands of the Cartesian Sea PIRATE (hat, length 6)
An Area With Big Stones and Rocks MONTERA (hat, length 7)
On The Runway COCKTAIL (hat, length 8)
In the Park BLUE (color, length 4)
Denver Botanical Garden LEMON (color, length 5)
Hall of Justice FOREST (color, length 6)
The Sixth Floor Games Lounge MAGENTA (color, length 7)
Audio/Visual Equipment Closet CHESTNUT (color, length 8)


Finally, indexing into the answers (first letter from the first word, second letter from the second word, and so forth) in each set, you get PINK (from the hats) and then BERET (from the colors), and PINK BERET is indeed the present for Piglet.