Learn Italian: Aspetto l'autobus davanti al museo. - I am waiting for the bus in front of the museum.

The phrase for "in front of" is davanti a. You must include the a before the noun. Because museo uses the masculine definite article il, the preposition a and the article il combine into the single word al.

Where is the word for "for" in aspetto l'autobus?

In English we say "wait for", but the Italian verb aspettare connects directly to the object you are waiting for. You don't need to add a preposition like per. It is literally translated as "I wait the bus".

Can I use di fronte al instead of davanti al here?

Yes, you could say di fronte al museo. Both translate to "in front of." However, di fronte a often implies being across from or directly facing something, while davanti a is a more general positional "in front of".

The translation says "I am waiting", but aspetto is just the simple present tense. Is that correct?

Yes! While you can use the present continuous tense in Italian (sto aspettando), Italian frequently uses the simple present tense (aspetto) for actions happening right now. English relies on the "I am doing" structure much more heavily than Italian does.