Definitely do not stay in your room.
1. ask the hotel to get you a half day orientation tour of the city. You get to see the layout of the city.
2. try a tour of Teatro Colon (about 10 blocks from your hotel)
3. During the day, BAires is very very safe. At night, I would take the usual safety measures that you would in any big city. It is overal very safe.
4. ask directions to calle Florida, pedestrian street with a mish mash of coffee shops, stores, Galerias Pacifico mall and a slice of Argentina life.
5. ask the hotel to make a reservation and call a cab to take you at night to cafe Tortoni for a tango show. ask them to order the cab to pick you up at night.
6. take a cab to Puerto Madero and walk around. stop anywhere for a great lunch.
7. Four Seasons has a really nice spa.
8. Walk to the Palace Alvear and enjoy a drink in the lobby cafe/bar. amazing architecture.
9. I echo the cementary visit. take pictures.
10. walk the Avenida Santa Fe which is very close to your hotel.
11. Even at midnight in Recoleta area, you see old (70's-80's) couples and single women walking alone in the streets and they don't seem to be very concerned.

enjoy.