Cemetery Recoleta – a famous Buenos Aires landmark. It's a major tourist attraction though the crowds disperse nicely beyond the main entrance.
Walk toward the Floralis Generica Sculpture and marvel at the large lotus flower.
Continue to walk through Recoleta – a neighborhood that makes you feel you are in Barcelona. Stop at Delicious for a shot of tasty espresso.
Get a cab to go to San Telmo and meander through the small cobble stone streets. Have (late) lunch at Cafe Rivas – an upscale, delicious affair. If you feel the lust for steak drop by Gran Parrilla del Plata instead for delicious steaks.
Nearby Plaza Dorrego has Tango dancers during most days – check it out.
Then get a cab or walk past San Telmo Park and the soccer stadium to La Boca. Marvel at the brightly colored houses and stay clear of the hagglers.
To chill out go to Frank's – a speak easy bar that only allows you to enter after you type a code into a fake telephone booth. Its a great looking place. If you are looking for a more hipster vibe look for 878 Bar.
Probably the best looking bar in South America is Milion in a old Recoleta mansion. It's a 15 minute cab ride from Palermo but it's worth it. Don't worry that you are late – every time before 2 AM is too early on weekends (midnights during the week) in Buenos Aires.