Havana, for the most part, is a very safe city, especially during the day. Locals are friendly and will often approach you to you/ask where you're from. From my experience, they are more than happy to give tips on whatever you are looking to do.
Plan to spend a day walking the colorful streets of Habana Centro and Vieja. Lonely Planet has a great walking tour that takes you through the plazas and most of the big landmarks like Plaza Vieja but, if you are like me and like to wander, just let your intuition guide you.
Life in these two neighborhoods is lived out in the street. Kids are playing, men and women are selling fruit and meat. Friends are conversing. Life is lived out in the open, not behind closed doors.
Vintage cars are a big part of everyday transportation. Most prevalent are 1950s American and 1960s Russian cars. You can hire a barbie pink convertible for an hour or a day and tour the city. If that’s too flashy for you, hop in one of the well-worn chevy taxi’s that have been painted a bright color and ride from neighborhood to neighborhood.
Make some time to visit the Cuban Art Factory, La Fábrica de Arte Cubano. It’s a reimagined peanut oil factory in the Vedado neighborhood that is home to some of Cuba’s best artists and creatives. There’s a bar downstairs with amazing mojitos and it regularly hosts bands like the Rolling Stones.
Walk along the Malecon, the shabby seawall that stretches from Habana Vieja to Miramar. Also known as Cuba’s largest sofa. You’ll see families, lovers, teenagers all hanging out and watching the sunset.
Casa de la Amistad and the Decorative Arts Museum are both in the Vedado neighborhood.
Take in music at La Zorra y el Cuervo, Gato Suerto or the state run Casa de la Musica