On the Sonic Adventure 2 disc, these files make up the texture data for the Chao Kindergarten area:

AL_STG_KINDER_AD_TEX.PRS
AL_STG_KINDER_BL_TEX.PRS
AL_STG_KINDER_CL_TEX.PRS
AL_STG_KINDER_CO_TEX.PRS
AL_STG_KINDER_DRUG_TEX.PRS
AL_STG_KINDER_HE_TEX.PRS
AL_STG_KINDER_HO_TEX.PRS
AL_STG_KINDER_LI_TEX.PRS
AL_STG_KINDER_OBJ_TEX.PRS
AL_STG_KINDER_PL_TEX.PRS
AL_STG_KINDER_PR_TEX.PRS
AL_STG_KINDER_TEX.PRS

These are, of course, PRS files, which can be extracted with Nemesis' PRS Decompressor. These uncompress into PVM's of the same name, and can be further unpacked into individual PVR's, viewable in any PVR viewer. I've extracted all of them and converted them to PNG, and they're available here. Here's an explanation of the textures contained in each PRS:

AL_STG_KINDER_AD_TEX: Misc. textures used in the lobby and in popup menus. The most intriguing is the Black Market one (see below).
AL_STG_KINDER_BL_TEX: Black Market. Not used the Dreamcast version.
AL_STG_KINDER_CL_TEX: Classroom.
AL_STG_KINDER_CO_TEX: Lobby.
AL_STG_KINDER_DRUG_TEX: No idea. Only three textures in it, which COULD be for a bottle. Leftovers for a drugstore maybe... ?
AL_STG_KINDER_HE_TEX: Health Center.
AL_STG_KINDER_HO_TEX: Textures for the actual Kindergarten building (which you see as you enter or leave).
AL_STG_KINDER_LI_TEX: Library. Unused!
AL_STG_KINDER_OBJ_TEX: Misc objects used throughout, including the Doors to different rooms. (No Library or Playground doors tho =/)
AL_STG_KINDER_PL_TEX: Playground. Unused!
AL_STG_KINDER_PR_TEX: Prinicpal's Room
AL_STG_KINDER_TEX: The textures from the Lobby (CO_TEX) and the actual building outside (HO_TEX). Probably used in early development as they were designing the kindergarten, but probably unused in the final.

The file kin_ade_moji1, located in AL_STG_KINDER_AD_TEX, contains the text that is shown above doors before you enter them. However, as you can see here, there are a couple that are not used:

Black Market, Play ground, and Library are not in the final! However, their textures still exist...

Black Market:
The Black Market was a place to buy rare chao and items. It was removed, but made an appearance on the SA2 Website that was accessible in-game. Later, it was restored in Sonic Adventure 2 Battle, the Gamecube rerelease.

The Black Market on the SA2 website (which was up before SA2B was released) has this picture:

This is probably a shot of the Dreamcast version, although there are virtually no changes between this and the SA2B version.

Library:
There's an unused voice clip from Omochao saying "You can download a new scenario of Chao Adventure from the library". However, there is no library in the Chao kindercarten. However, there are several textures (cs_mouth05 & 07, cs_statue_01, cs_steye_01 & 02, cs_wall - maybe cs = Chao Statue?) which closely resemble the Chao statues in the Chao Race lobby. Also, there are several books labeled 'Album' (kin_koalbum 1 - 4). Perhaps these were for saving snapshots of your Chao? Also, there are several other books: Health (kin_libook1), Beauty (kin_libook2), and Fortune (kin_libook3). Tutorials, probably. There are also several wood textures, and shelves of books, plus some textures that strongly resemble a computer (li_paso 1-5 - 'pasokon' is Japanese for 'computer').

kin_libook1 - 3

kin_lipaso1 - 5

Finally, there are 2 leftover models of the Library room. Since the model format of SA2 has been cracked, forum member ultima espio managed to rip the models from the disc. These are what the the library might have looked like:

Playground:

Note the circled picture.

This is located in the far right corner of the Kindergarten lobby, right next to the Health Center. Here's the texture the picture uses (kin_cophot2 in AL_STG_KINDER_CO):

This is the only picture we have of the Chao playground. How do we know it's from the playground? Looking through some of the textures in the playground PVM, you'll notice that several of them seem to match up:

Key:
1 - CASCADE_A00: Most likely. There definately WAS a fountain there, as you'll see in #7
2 - KIN_HOGRASS: It seems to fit.
3 - KIN_PAKIA01: Bark from the trees. 'ki' is the Japanese word for tree
4 - KIN_PAKIA02 and 03: Once again, 'ki' = tree. It definately looks like it would work.
5 - KIN_HO_YAMAA: Background trees, same as the ones used on the path to the Kindergarten. 'Yama' = mountain(s)
6 - KIN_PAHEI & KIN_PAHEI2: Used as the wall around the playground, probably. 'hei' = wall/fence.
7 - KIN_FUNSUI (1 -9) (funsui8 is the one I used in the picture): These were the textures that really convinced me. 'funsui' = fountain.