内 works as a suffix or as a standalone noun, similar to the English inside (e.g., inside a car/the inside of a car).
When used as a suffix, 内 is read ない (always, I think). As hiroki's answer suggests, it connotates the 'building'-ness of the preceding noun.
That is, 保育園[内]{ない}で sounds in the building of the nursery while 保育園(の中)で sounds broadly in the nursery.
Other examples of 内{ない}
- 時間[内]{ない}: within the time limit
- 期限[内]{ない}: before the expiration
- 校[内]{ない}: inside school building
When used as a noun, 内 is read うち. For example, 内{うち}と外.
Also note that when talking about inside X(location), Xの内{うち} is not used. It should be Xの中. (For non-location, 計算の内{うち}=expected (lit. within calculation)).