I have to play next month in a restaurant. Could you give me some good pieces to play?
Here are some of the "must know" songs and pieces for restaurant/lounge playing in the USA.
Songs from...
Phantom of the Opera
Evita
Les Miserables
As Time Goes By
Misty
Memory
Moon River
The Rose
Satin Doll
The Shadow of Your Smile
Music Box Dancer
Harbor Lights
Linus and Lucy ( da Snoopy Dance)
Yesterday (Beatles)
Raindrops Keep Fallin' on my Head
Always and Forever
Beauty and the Beast
Chances Are
My Heart Will Go Under

(Titanic theme)
Mandy
Unchained Melody (theme from "Ghost")
Send in da Clownz
That should get you started. You never know what people are going to ask for, but if you learn these pop songs you'll have a good foundation. BTW to be successful at this you MUST play requests, to the best of your ability. And when the manager tells you you are playing too loud, pipe down. You'll figure out how to play the room after a couple times, how to play in such a way that you are not obtrusive. At my current gig ( six years and five months) I leave the lid on the piano (Kawai 6' 00") completely closed, so I can play normally without being too loud, laying the music (when I need it) flat. The music stand is bad if you're using music, you don't want to look like you're practicing. Also, people want to see you (whether they're looking or not). You are part of the decor, so dress nice and smile

. Welcome to "furniture music", as Satie called it.
Make sure you have a mix of styles to play, although you will evantually find your own balance, and select a default. Mine is jazz, I play a lot of jazz standards and modern jazz pieces, but I can play the show schlock, post 1964 pop and classical pieces (of course). When people request something you don't know, learn it, it will probably come up again. Happened to me tonight, a man asked me if I could play anything from the Broadway show "Wicked" for his daughter. I apologized and said I didn't know the show, and asked him if there was anything else the little girl might enjoy (always do this when you can't play a request). He said "Disney tunes" and now I have $30 I didn't have five hours ago.
For classical rep, look at one of those "favorite Classical Piano Pieces" albums and start with those pieces. My most requested classical piece is "Clair de Lune", followed by Fur Elise (kids like it). People usually just ask "can you play any classical?", which puts that ball in your court.
You will need to build up selections of songwriters, often people ask "play some Cole Porter" or "play some Gershwin" and I am happy to oblige, as this is the music that I enjoy the most in this situation. To get you started...
Gershwin: The Man I Love, Someone to Watch Over Me, Embraceable You, They Can't Take that Away From Me, Summertime (this one comes up a lot), A Foggy Day, I Got Rythym.
Cole Porter: Begin the Beguiine, Night and Day, I Concentrate on You, Easy to Love, I Get a Kick Out of You, It's Delovely.
Jerome Kern ( perhaps the greatest of these composers): All the Things You Are, Old Man River, Smoke Gets in Your Eyes, I Won't Dance, Yesterdays.
Don't know how applicable my rep suggestions are outside of the USA but this is what I know works here. You'l find that my basic principles will work for you, you may have to tailor them geographically. Let us know how this works out!