Why not? Just go to Israel or your nearest synagogue.
Interestingly, I ran across this in an Art History textbook which had a discussion of why early artists painted Jesus the way they did. It's conviently left out of all of these "what did Jesus look like" articles. The following description comes from Pubulius Lentulus, an associate of Pontius Pilate,
"In this time appeared a man endowed with great powers. His name is Jesus, and his disciples call him the son of God. This Jesus is of noble and well-porportioned stature,with a face full of kindness, and yet firmness, so that beholders both love and fear him.
His hair is the color of wine, straight and without lusture, but from the level of the ears curling and flossy. His forehead is even and smooth, his face without blemish, and enhanced by a tempered bloom, his countenance ingenuous and kind.
His nose and mouth are in no way faulty. His beard is full, of the same color as his hair; his eyes blue and extremely brilliant. ...
His person is tall, his hands beautiful and straight. In speaking he is deliberate and grave, with little given to loquacity; in beauty surpassing most men".
And you'll see a wide variety of appearances.
If you did that you'd see a odern-day Jew. He might be "Ashkenazi" or he might be "Sepphardic"; we also don't really know how much genetic drift has taken place amongst the Jewish population over 2000 years of diaspora and pogroms. So you may or may not get a very good idea at all of what Jesus looked like from looking at a modern-day Jew.