What should I do when I wake up impure and miss the prayer time because I am waiting for the bathrooms to open?

If a Muslim knows that the restrooms will not open until after the time for prayer has expired, then he must seek another place for purification. If he does not find one, then his obligation is Tayammum, as he is considered to be in the status of one lacking water. However, if he hopes that they will open and water will be available before the time expires, then he should wait.

Imam An-Nawawi mentioned that there are three situations for one who lacks water: 1. Certainty of finding water at the end of the time: It is preferable to delay the prayer so that it can be performed with ablution, because ablution is more complete than Tayammum. 2. Despair of finding water at the end of the time: It is preferable to perform Tayammum and pray at the beginning of the time, without dispute, in order to attain the virtue of praying at the earliest time. 3. Uncertainty about finding water (but hopes to find it): The more correct view is to offer the prayer with Tayammum at the beginning of the time, even though there is another opinion to delay it, which is the view of the majority of scholars.