Hmm. A few places spring to mind that fit some of those criteria, but it'll be hard to accommodate all of them in one place, so something might have to give.
If your question had come in a couple of years ago, our top recommendation would probably have been Capozzoli’s, a classic old-style Las Vegas Italian restaurant that was located at 3333 S. Maryland Pkwy. and an established favorite with the entertainment crowd (Tom Jones was known to show up and jam from time to time after a show). The décor was casual, there was a bar, and it served decent traditional Italian fare until late. The main draw was the atmosphere, however, and it featured dancing nightly to the strains of a live band performing jazz standards, Sinatra songs, etc.
Sadly, Capozzoli's burned down last year and hasn't reopened. So we put on our thinking caps and came up with three other suggestions.
"Evenings feature live entertainment beginning at 7 (good jazz groups and the like). The music extends past midnight, when an after-shift late-night crowd shows up. The décor is old Vegas. The patrons are old New York, Chicago, and Detroit. There's even a decent slot club with daily hot-card promotions and potential free-play vouchers via the mail. The video poker schedules are in the 97% range at best (e.g., 6/5 Bonus), but just putting $40 in the machine gets you a comp from a good player’s menu, plus your drinks."
There's a bar, which we're sure serves martinis, although we couldn't vouch for them being "killer," as we've stuck with beer and wine when we've visited. It's mainly old-style booth seating, with tables in the middle, but they offer a banquet service and are used to catering big parties -- just give them fair warning about your big party, so they can arrange things for you appropriately (702/384-4470). Oh, and they also offer a free limo service, which might be fun for your party (ask about it when you make your reservation).
"The food? It's good. Steaks range from $32 for a petite filet to the $65 28-ounce porterhouse (most are $37-$42). Italian specialties are $24-$29, appetizers are $12-$16, sides are $5-$8, and cherries Jubilee or bananas Foster prepared tableside go for $12. You’ll like the meal, but the food definitely plays second fiddle to the joint."
This is the the priciest of the three joints we're recommending and it's not Italian, but there are plenty "Italian Specialties" on the menu and they do have two private dining rooms, one for up to 42 and one for up to 18, which could be perfect for your party. Give 'em a call and see, if this sounds like it fits the bill (702/384-4470).
Suggestion #3 is the Bootlegger Bistro (Local Corner Aug. 2003). The original restaurant, which opened in 1972 at Eastern and Tropicana, is gone; the new location is next door to the Belz Outlet Mall. Here's the gist of what we said about it in 2003, updated to reflect a few changes. "You can get a good plate of pasta at the Bootlegger, but that’s not what sets this place apart. This is one of Las Vegas’ truly 'in' night-spots —- a place where showpeople from all over the city gather to relax and sometimes jam. ... There’s live entertainment nightly, with open mic nights for 'special guests' (generally performers from production shows around town and sometimes headliner talent) several nights a week." The Bootlegger serves food around the clock, with a discounted late-night menu (11 p.m.-6 a.m.) that includes pasta dinners for as little as $6.95. Regular-hours prices run $12 to $20 for pastas and under $30 for veal and steaks. They have a couple of private dining rooms if they can't accommodate you in the main restaurant.
The final suggestion comes from a reader who saw today's answer previewed yesterday and wanted to make sure we didn't leave out Carluccio's Tivoli Gardens, which also happens to be a favorite of an LVA staffer, who had this to say about it: "Carluccio's is indeed old school. The spaghetti is good (not great), but the atmosphere is ridiculous. The owners haven't redecorated since the property was owned by Liberace, so there's a VERY dark bar area, a private room with a mirrored piano, the main seating area has an atrium with fountains, and a few side rooms for patrons which feature palm-frond wallpaper and those awesome peacock rattan chairs from the '70s. "I've been eating there for more than 20 years on the strength of one dish: chicken livers tarragon -- chicken livers sautéed with loads of garlic and tarragon with mushrooms over linguini noodles. They also make good gnocchi as well as cavatelli with meat sauce. The food is not gourmet, it's work-a-day Italian, but it's quality and the place has great character."
Good luck, have fun, and let us know where you go and how it works out for you.