Will be staying in NYC in early July (After the 4th) are there any great late night after dinner hang-outs? (Not Clubs)I would love your suggestions

Your best bet would be to check out the restaurants and bars along both Columbus Ave and Amsterdam Ave between 79th st & 86th St. Places like Calle Ocho @ Columbus & 81 or 420 Bar @ Amsterdam & 80 or Venue @ Columbus & 84
would be great places to start. There are many more, again, the Aves. I mentioned will have the greatest concentration of places to go.

Drip (coffee and dessert bar).

How about Cafe Lalo, a dessert cafe on 83rd street between Broadway and Amsterdam. As Anthony mentioned, that area is also filled with lots of bars if that's what you're looking for.
Also, the Barnes and Noble (w/very small 'cafe" is a block or so away, and is open till 11pm weeknights, midnight weekends. It's a popular neighborhood hangout.

Cafe Lalo is great, also Cafe La Fortuna on W. 71st St between Columbus & CPW. For pubs/bars there's Dublin House on W. 79th and way uptown is my friend's favorite, The Abbey on W. 105th between Broadway & Amsterdam.

If you like live music also uptown on Broadway & 105 is Smoke (jazz) and on W. 79th St is Wilson's.

Unfortunately, Wilson's has closed.

How about French Roast? I'm an East Sider and I forget exactly where it is - 80s and Amsterdam?

French Roast (a restaurant/cafe--open 24 hours) is at Broadway and 85th street

Wilson's closed? Sigh... I just walked by and I thought I saw their name still up but maybe it was just the Lucerne's sign. Some nice memories of time spent there. Some folks we know go to the Evelyn's basement lounge to meet their friends (on Columbus and 78th).

Wilson's name is still up but it is closed.

French Roast is the worst, rudest spot on the UWS. Only go if you want to be fuming after incredibly poor service(had to wait over 1 hour for the check on a dead night) and mediocre food.
Much better are Anthony's recommendation. I would add Potion, Cafe Mozart for dessert, The Heights for margaritas on the roof if you are WAY uptown(111th and Bway). Drip is sort of a singles bar--they keep binders of people you can meet up with. Try www.newyork.citysearch.com for a comprehensive list.

Ditto on French Roast. The place is a disaster. Avoid the Heights unless you're a student. It's full of margarita sipping students getting wasted into the wee hours! Try Cafe Edgar on 84th for amazing desserts. I can't believe wilson's closed. That place was perfect!

We UWSiders were quite surprised to see the sign out front stating they were closing. I believe NY1 did a story on them a couple of months ago. Yup, very sad. We loved that place.

By July, the Heights should have almost no students, certainly not undergrads. It becomes much more local in the summer.