Pianos are not so noisy that your neighbours will be that disturbed.
A simple comment one day that your daughter is learning will suffice to avoid problems.
I would suggest that you invest in a decent piano stool because height for your daughter will be an issue.
Secondly I would suggest that you buy a couple or a few Tutor books, (A decent music shop will advise or try the 'net). Try your daugter on these for a while (and yourself, maybe). See how she takes to the rigour of regular practice and the determination to continue trying to master difficult techniques (because everything is difficult and strange to start with). She'll also be learning to read music.
A metronome is an important tool. Look for one with a light also to indicate the beat. Sometimes you may not hear the beat but will see the light flashing. (Again a music shop will advise)It's acceptable practice to slow the metronome down to a pace that a phrase can be played then bring the speed gradually back up to correct speed. But this isn't going to be an issue for a few months yet.
Finally, if all the keys are playing properly on the piano, don't worry too much about a tune-up. Not at this stage in your/ her music career.
In my experience any work is priced according to the amount of work that is required. In a couple/few/six months, you'll have a feel for how much work will be involved. Perhaps I ought to add here that "hearing" the correct notes is important in a music students learning, but as long as the notes are reasonable at this early stage, don't worry too much.
Check out this site:
http://www.parentsmusicguide.com/2008/04/what-is-the-average-cost-of-piano-lessons/
Incidentally, in a few years, perhaps at the advice of the school or teacher, think about seeing if your daughter will add another/secondary instrument to her 'portfolio'
A piano is often a solo instrument, especially when learning, whereas learning another instrument gives increased opportunity to learn/play in a group/band. This helps the musical development and provides more entertainment/amusement in the learning process.