I have a group of 3-4 friends who get together and play for each other, just to get used to playing for someone other than ourselves and our teachers. I second all of Lelle's recommendations - I've played at nursing homes and gotten small gigs in churches. Where I live, anyway, there are so few available pianists/organists, that if one gets sick or goes on vacation, churches are super grateful for anyone who can handle it - and it can mean nothing but playing a prelude, interlude, and postlude (using pieces you already know) and playing the hymns, if necessary, just plunking out the melody to help the congregation. I also do a house recital in my living room for 15-20 friends every year. I'm no great shakes, didn't start piano until I was 40 (though I had other musical background), but I still find people appreciate my very modest talents.
You are definitely thinking the right way - the more you make yourself deal with the stress of playing for others the easier it gets, and if you are not trying to make a career of it, there's nothing terrible waiting for you even if something does not go well. And forcing yourself to play for others and have recital goals can be pretty motivating and make you progress faster than you might otherwise.