We will be in NYC this weekend, and would like to see the new MOMA. Friday night is when it would fit into the schedule, which happens to be free night from 4-8 pm. Is it still swamped? What kind of wait should we expect? Better to go before or after 6?

It is going to be packed to gills.

We went a little bit after 6 a few fridays ago and had no wait at all. There were a lot of people inside but I would not called it "swamped". We really enjoyed it.

I went this past Friday just before 5, and gave up because the lines were massive BUT it was Good Friday and schools were off, many more tourists than usual, etc.
Friends have told me that later is better than earlier. 4-5 is busy with the people who have been waiting on line since before 4, and 5-6 gets the running from work crowd. By 6 or 6:30 things begin to move more reasonably.

The later the better, but, of course, the later you go, the less time you have to see the art!

Go late and head directly to the 5th floor if you want to see the amazing permanent collection.

What about the restaurants there? Are they good, or just convenient and institutional?

Surprisingly, the restaurants at MOMA are pretty good. We especially like the cafe on the second floor: The prices are reasonable, the service is good and fast and the food is good. Don't be thrown off it there's a line. It moves very fast.
We've not tried the other two restaurants; however, we've heard that they are good (but more expensive).