Besides eating currasco (grilled meats) and drinking chimarrão (yerba mate tea), another essential eating experience in Porto Alegre, in my opinion, is lunching at a "galeteria". This typically local style of restaurant, which came to Porto Alegre with its many Italian immigrants, serves spit-roasted chicken with all the trimmings - pasta, salads, rice, beans, etc. Huge amounts of food, and normally fabulously juicy roast chicken with crispy, crispy skin.
The well-known Brazilian gastronomic review, Veja, awards top honors in its 2001 edition to the "Galeteria Veneto" with two locations in Porto Alegre. I'm not personally familiar with it, but Veja's awards are generally quite reliable.
celfie you have gotten a lot of good Rio suggestions, but its still worth searching the archives as there are a lot of great reports including a great thread talking in length about Santa Teresa in Rio.
I didn't see any suggestions for restaurants with food from Minas Gerais which is worth looking for while you are in Rio. One place I have been A Mineira in Botofogo which is a large buffet letting you try a number of dishes (they also had an afternoon rodizio of petiscos), but they did a lot of expanding (mostly to far away places) and not certain if the Botofogo location is still open or now not associated with the rest. In any case if you don't get favorites from hounds, ask around for recs in Rio or ask someone to call the number for A Mineira. If you want something to compare Rio and Rio Grande do Sul you could look for costela no bafo (vapor cooked) which is really popular around the periphery of Rio (not certain about tourist areas, I have seen it more out beyond Niteroi, on the Ilha do Governador, etc) and a costela no fogo do chao both beef rib dishes (you could also try the plate vaca atolada of beef ribs stewed with yuca from minas gerais and goias for more beef ribs).
A destination to consider is the Feira Nordestina in Sao Cristovao in the Zona Norte, lots of food, music,etc. During the recent violence there was a couple of car and bus hiijackings in Sao Cristovao (the favelas the police occupied are north of there). There haven't been many since, the highways are being patrolled much more intensely than before, and to be honest the troublemakers are probably far from the zona norte right now, but since its only just calmed down its worth seeing how things are on the ground before going (and your hotel, etc may discourage you as a matter of course).
Portuguese/Brazilian: Antiquarius, it's really good, don't miss it. It's considered one of the best restaurants in Rio and IMO it is true... The place is a Rio institution and it has been around for a long time. But Portuguese food can be very unfamiliar to lots of people; an American couple friend of mine hated their signature dish: cod fish with eggs, exactly because of the eggs... But that's Portuguese... It's expensive though.
Ice cream: Mil Frutas - as the name says, 1000 Fruits. You can taste ice cream made with different kinds of tropical fruits. White chocolate and passion fruit is my favorite. They have 3 locations: Rua Garcia D'Avila, Rua J.J. Seabra and in a mall in Leblon. Don't miss it!
Juices: Brazilian juice stands are amazing. My favorite is a store in Ipanema, Polis Sucos, Rua Maria Quiteria with Rua Visconde de Piraja. Don't miss it!
Steak House: Not Rodizio style, but the best meat you can get in Rio, Esplanada Grill, Rua Anibal de Mendonça
Kilo: try a kilo, you pay buy the weight like in a NYC deli, but the experience is quite different, waiter service, great food. Fellini in Leblon is very good. It's a good way to try different Brazilian dishes since it's buffet style. Another good kilo is Fronteira, they have in different locations, there is one close to the Hippie Fair in Ipanema, Praca General Osorio.
Cozinha Contemporanea (a kind of "New Brazilian" Cuisine, traditional ingredients with a fancy twist): Carlota (try the cupuaçu mousse or the goiabada soufle for dessert!), Atelier Culinario, Careme Bistro or Roberta Sudbrack (supposed to be excellent, but quite expensive).
Go to a Botequim after the beach, as the cariocas (people from Rio) do: Bracarense and Manuel e Joaquim are 2 good options. You can have salgadinhos (Brazilian savory snacks) and beer. Manuel e Joaquim has dinner too. Bracarense is located in Leblon and Manuel e Joaquim has different locations in the city.
Italian: In Ipanema: Gero (more expensive, nice room and great people watching) and Artigiano, inexpensive and very good, but cash only.
Fasano al Mare: really high end and expensive; if you want a splurge it's the place to go. I have only been to the one in Sao Paulo and it was quite wonderful. It's the same owner as Gero.
Light food/salads: Celeiro in Leblon
Alessandro and Frederico in Ipanema has very good contemporary food and pizza.
Gula-Gula: it's one of my favorite place for desserts and they also have wonderful salads. You can also find more hearty dishes there, so if works for both lunch and dinner. If you go don't miss the petit gateu de doce de leite with tapioca ice cream. One of my favorite desserts.
Drinks: Academia da Cachaça, Leblon. You can taste different kinds of cachaça, the liquor we make caipirinhas and batidas with.
Pizza: Cappricciosa and Braz. Don't miss Brazilian pizza, it's quite good.
Try a tapioca. They sell on carts on the street. It's a kind of crepe made with yuca flour. Really tasty. You can also find at the Hippie Fair with other tapioca snacks and food from Bahia.
Degrau: Leblon. This restaurant has been around forever and serves traditional Brazilian food. Inexpensive. They have a huge menu with fish, pasta, chicken and beef options. I would compare it loosely to an American diner, but not quite...
Have fun in Rio. Can't help you with Porto Alegre, I haven't been there in quite a while.
I second Antiquarius and Polis Sucos (the drinks and the sandwiches). Bibi Sucos on the Ipanema/Leblon line is rated the best right now though I believe but I am partial to Polis Sucos.
I like Marius more than Porcao because it feels more authentic and more laid back but honestly to me they're a push as you should stick mainly to the picanha with garlic at either.
I think Gero and Fasano Al Mare are good but not great (more style than substance) and the best Italian in Rio is D'Amici in Leme/Copacabana (the lamb special with pasta is amazing). In Ipanema options like Mio and Terzetto are also quite good and though they lack the atmosphere of Gero et al. they have better food, IMO. Terzetto is also a great place for oenophiles as their sommelier has been voted the best in Rio and they have an extensive list of South American wines. Quadrifoglio in Botafogo has changed its chef within the last year and reviews have been excellent though I have not been since the change.
For contemporary cuisine I think Olympe is the best (the chicken with farofa is unique and outstanding) though it is a splurge. I was very disappointed with Roberta Sudbrack. It was good but to me tried too hard to be fancy and innovative and was not in the same league as Olympe. Carlota and Careme were good but didn't wow me and were a step below Olympe (and last I checked Carlota doesn't take reservations and is not a big space so there is always a wait).
If anyone is interested in sushi I have heard great things about Azumi in Copacabana.
For drinks I like going to any Devassa and getting a caipirinha. Cheap, simple, classic, cold, awesome.
There are many Rio reports that have some great material that you should find very helpful.
Porto Alegre?The state of Rio Grande do Sul is churrasco country.
For churrascaria, try Braseiro or Na Brasa.
Go to Bah for contemorary Gaucha cuisine, from the state of Rio Grande do Sul.Also Estancia de Sao Pedro, which has live music.Vitrine Gaucha, a buffet with 22 meats, get the arroz carreteiro.
Hit up some botecos(pubs) and a chopperia like Caverna do Ratao. Lanchonetes will be everywhere.
regarding Rio, you can check
What kind of food would you like to have?
What about your budget?
If you want to upscale in a stekhouse or as we call it "rodizio"(all-inclusive but beverages), you must go to www.porcao.com.br, and I would suggest the Porcao Rio's branch with views from Baia de Guanabara.