Piegari is very good.
There is another restaurant in the same little area (La Recova) called El Mirasol that is also quite good.
If you want to try something that is a little more local and less touristy, try La Amistad in Palermo (on Fray Justo Santa Maria de Oro not far from the US embassy).
Gardiner is also quite good and has a nice deck on the river (located at Av. Rafael Obligado and Costanera (La Pampa)). If you're going soon it may be too cold to sit outside as it is Winter in Argentina.
A note about restaurants in Argentina. Most do not open until at least 7:00 and you will not see a significant number of people there until 8:30 or 9:00.

I would add Fervor to Tengohambre's excellent list.
Fervor has the same owner as Sottovoce but offers more grilled dishes, especially fish.

shhh. Do not talk about Gardiner por favor....it is a very good restaurant that remains off the radar of tourists...keep talking about it on Fodors and there will be as much English as Spanish spoken by customers...:)

Congratulations on your honeymoon and what a good choice, BA really is a romantic city..! It has something for everyone in terms of taste, budget and location so you'll be in the right place! Just Palermo alone has 600 venues for wining and dining, if you're looking for a complete romantic evening and a good idea of Porteno culture you ought to spend a night at a Tango show, I would strongly recommend Boca Tango or El Almacen... both include a typical Argentine dinner, El Almacen is probably more elegant, but Boca is perhaps a more "authentic" neighbourhood! Both of which can be booked online...Besides that my favourite restaurant in BA is "Osaka" a Peruvian-Japanese fusion!

Have a great trip!

I go to La Cabrera every time I'm in Buenos Aires and I LOVE IT!!! The steaks are HUGE. Gigantic. Like 20 ounces per piece of meat! I didn't find it to be touristy at all. No one spoke English except the people I was with (and myself, of course). It's in a great neighborhood and the food is absolutely amazing. I won't go to Puerto Madero to eat as that is very touristy. I also LOVE Cluny (nice rec, Scarlett!).

the best meals we had were at tiny places or old favorite argentine places....the big name places left us flat...

of course our best meal was at avrooster's house...