After one year of lurking on this web site, this is the post that prompted me create an account. Please don't change your plans because a few people on this site have had bad experiences in San Telmo. The ones who are scared of the neighborhood don't live here. I have a friend who was robbed three times in one month, and guess where? Las Cañitas, Palermo Soho, and Las Cañitas again. It can happen anywhere. Don't walk around with a camera dangling on your wrist, walk like you know where you're going, and since you are only here for a week you will probably be fine, just like all the other tourists who leave loving it here.
In my opinion, San Telmo is the ideal neighborhood for a short-term stay. I live here. Walk to the Casa Rosada and other historical buildings near the microcentro? Check. Feria San Telmo on Sundays? Check. Short cab ride to La Boca to see El Caminito and the Proa, the modern art museum? Check. (Just leave before dark). Museum of Modern Art on San Juan between Defensa and Balcarce? Check. Delicious dining options? La Brigada is one of the best parrillas in the city. Territorio on Estados Unidos y Bolívar has great sandwiches and picadas--huge portions for a good price. Cafe San Juan is all the rage--make a reservation. El Baqueano has a great tasting menu with exotic Argentine meats. Shopping? San Telmo has great antique stores, funky boutiques and a great indoor market with antique vendors, great fruit and veg stalls and various butchers open every day of the week. It's a great place to take pictures. Nightlife? There's bar on every other block.
Puerto Madero and the reserva ecológica are walking distance, if you'd like some luxury and/or nature. Biking through the reserva has been on my list for years, and there is a bicycle rental place called La Bicicleta Naranja that will set you up. Eat a choripán on the Costanera Sur. Bellas Artes and MALBA museums are not far by taxi. Neither is Recoleta--the cemetery and a nice stroll are highly recommended.
Not sure how old you are, but my parents are both 60+ and loved staying in San Telmo. So did a lot of their friends, who also chose to stay in the neighborhood. I would recommend Hotel Babel, a boutique hotel on Balcarce between Estados Unidos and Carlos Calvo. It's on a beautiful, quiet, cobblestone street. Stay in Palermo if you want to go out until 6 in the morning and eat American-style brunch when you're hungover. Stay in Recoleta if you want upscale elegance. Stay in San Telmo for everything else.