Churrascaria Palace
Rua Rodolfo Dantas, 16 - Copacabana
(next to the Copacabana Palace Hotel)
Price: 47R per person (37R w/coupon)
Expected Bill: 100-150R (depending on drinks and deserts)
Website:

http://www.churrascariapalace.com.br/abertura.htm

This is one of the better Churrascarias in Zona Sul in my opinion. And for the price (37R with coupon), it is much better value than lets say Porcao. It is hard to beat views of Porcao Flamengo, but if you don't feel like wasting time and/or money then this is great option right in Copa.

I think it is better date place (than Porcao Ipanema and the Caretao's) as it is a little more quaint generally with a guy playing a piano and flatscreens showing a soccer game. The other places can get really noisy and busy depending on the night of the week. Also, when I go out for a nice dinner I get tired of seeing a stupidly dressed gringo (white high-top tennis shoes and shorts) with his favelada date of choice for the evening. That seems typical at a place Marius or Porcao, where this place seems to be mostly well-mannered Brasilians.

As for the food, again I think it is on par with the best Churrascarias. It is a bit limited on seafood, but ask for the trio of Octupus(Polvo), Lula(Squid), and Shrimp (Camarao). All tossed in garlic and oil. I used to be able to order Langostinos (large Prawns), but my last visit they said they did not have anything. They do have raw sushi and oyster bar. As for their meats they have them all, but I would recommend to special order the Baby Bife and Picanha Nobre.

If you forgo alcholic drinks and desserts, you and your date can get out of here for about 100R and completely satisfied.

For drinks, I would recommend going next door. There is nice little sportsbar to hangout if there is decent game on. It is called Mug Bug.
They claimed to have over 50+ kinds of bottled beers. You can order typical cocktail drinks like a Mojito or Mai Tai without being look at strangely.

Mud Bug Sports Bar

http://www.mudbug.com.br/