Don't worry about the "unfamiliar grand"; yes, you will get a few unexpected feels/sounds, etc., but you yourself will be amazed at how quickly you will get used to it, so expect to struggle a bit for the first few lines, but after that, you won't have any trouble concentrating on the music, simply because you will be so fully occupied with the job at hand that the piano will be the least of your worries. It is therefore important to practice the first few lines very well; every chance you have, play these few lines without any warm up, with cold hands. Everything tends to go very smoothly once you get a good start. However, you need to be concerned about the concert hall; a hall with good acoustics will absorb all the sound from the piano, so you may have difficulty hearing your own playing; in fact, if you put the music stand up, you may not hear anything! So make sure the stand is down or removed.
Most performers get most nervous just before they play; once you start, you will immediately become so pre-occupied with playing that nervousness will fade into the background. Knowing this is not only reassuring, because it happens to everybody, but you can use it to further suppress nervousness. It also helps to know some basics:
Do not over-practice on recital day. Some teachers allow their students to practice at (near) full speed (never over speed) only once, and medium or slow speed several times before exams or recitals. Always play the performance pieces slowly or medium speeds (doesn't have to be very slow unless you are unsure of memory). Do not try to learn anything new for couple days before recital, but you can play anything you have learned previously, especially to keep the fingers warmed up and ready to go.
Most important, you should be conducting mental play, playing the piece in your mind, away from the piano. If you become good at it, you can play it in bits and pieces, from anywhere in the piece, one hand at a time, or both together. This is most useful for getting rid of nervousness before the performance, when you are waiting with nothing to do. Try mental play to make good use of this extra time. Be sure to bring the music, because if you get stuck during mental play, you can look it up and fix it.
Lots more detail in my web page link below (over 300 pages!).