Here are a few more suggestions:

Il Vagabondo on East 62nd Street in Manhattan. The food may be a little pricey but its handmade pasta and nice sauces make it work the trip. The added touch is that there is a regulation bocce court right in the restaurant. I think you can use the bocce court if you are a diner but I have never asked or tried.

http://www.ilvagabondo.com/html/menu.htm

You can also rent out the place for large parties like F-T dos. Here's some info on that:

http://www.ilvagabondo.com/html/info.htm

One of my favorite and less expensive Italian restaurants is right by Times Square called Simply Pasta:

http://simplypastanyc.com/media/simplypasta.html

The pastas are made in house and are very good. Plus the decor is pretty fun and funky with dark colors and giant flying ceramic pasta coming from the ceiling.

I've hosted a few F-T events and Dos at Simply Pasta and as far as I know eveyrone's been happy.

Of course it's not Wollensky Grill but who can resist giant flying pasta!