Fashionista here! (is that too ... Yeah...)
Anyway—
It definitely depends on the restaurant. There are several types:
Casual dinner
Formal dinner
Dinner dress casual
Black tie (if you're ritzy, I doubt I must inform you too much but it simply means men wear black dress cost, tie, and a white dress shirt with black slacks)
And many more!
I'm assuming it will be more casual since it is only a birthday dinner.

For a clean look, I would say wear a button up dress shirt (any colour but I advise against neon colours unless you're going to wear a black jacket and try to pull off a scene look) and dark blue denims. Corresponding shoes are advised lol. Or you could wear a nice polo shirt or anything up that has a collar, it looks clean. I personally love plaid (part hillbilly, don't blame me

) and if you don't wear prescription glasses, fake or unprescribed glasses (square or rectangular) make it look so much nicer.
Also, if you take my advise and wear a long sleeved button up shirt with a dress coat, folding up the ends of the dress shirt sleeves (if they are long enough) over the ends of the coat (if it is short enough) would look nice and kind of youthful (in going to guess you're in your 20s)