Need help choosing please
Do you already have reservations for all three? Are you booked at the NoMad with a capital M, or the other one?
What kind of atmosphere do you seek? The NoMad is probably the comfiest one of the three.
When is the meal? Blue Hill around now may not be as interesting as in the summer/early fall.
Totally depends what you want, as they are three very different places.
Minetta is fun. The food is fairly elemental but extremely well prepared French bistro fare. The atmosphere is boisterous -- but in a rather adult way.
The NoMad is swank in a very enjoyable sort of way. I think the food is less interesting than it thinks it is, but it's very good. While the NoMad purports to be more "grown-up" than Minetta, to me it's more for younger people playing "dress up" as adults. I've never had less than an excellent time there, though.
Blue Hill is virtuous. I don't like it, personally. But if you want farm-to-table, prepared in a way that honors the ingredients, it's the top of the NYC heap.
So my bottom line: if you want a fun birthday, Minetta. If you want a fancy birthday, the NoMad. If you want to stave off aging by eating food that's good for you, Blue Hill.