I play for a lot of older clients (but not at senior centers) and yes, I use midi files extensively. A few suggestions from my songlist:

Moon River, On The Street Where You Live, The More I See You, Unforgettable, The Way You Look Tonight, Fly Me To The Moon, I Can't Give You Anything But Love, Shangri-La, Autumn Leaves, Stardust, The Nearness of You, Days of Wine & Roses, Girl From Ipanema, I've Got You Under My Skin, Moonlight in Vermont, A Nightingale Sang in Berkely Square, Thanks For The Memories, All of Me, Misty, Sentimental Journey, Satin Doll, Bewitched Bothered & Bewildered, I'll Be Seeing You, The Sweetheart Tree, Polka Dots & Moonbeams, They Can't Take That Away From Me, Someone To Watch Over Me, Skylark.