The basic answer would be the same, even if you were a beginner.
You may, indeed, strike up a conversation with a random stranger in the US.
Sí, puedes entablar conversación con un desconocido escogido al azar en EEUU.
I'm answering based on personal experience. When I returned to the US from living in Mexico, and was suffering from culture shock, I was glad to find other Spanish speakers to talk to, in a variety of states and walks of life and situations. They were glad too.
On the other hand, later on, returning once again to the US after living elsewhere for some time, but in this case, France, I found it difficult or impossible to chat with strangers in French. If the person was from France, I didn't get anywhere, and felt flattened by my attempts. If the person was from Canada, things went better; if the person was from Africa, the experience was as comfortable, and rewarding, as with Spanish.
Here are the reasons I can think of, for why most Spanish speakers respond positively:
Living in the US can be quite alienating for a Spanish speaker, especially if they get frustrated when communicating in English. This is true even if one's documents are in order.
The US is a place where many different regional variants of Spanish come together. Participating in this linguistic melting pot is thrilling.
Most Spanish speakers (at least those from Latin America -- I have less experience with Iberian Spanish speakers) are extremely encouraging of new Spanish speakers, and tolerant of mistakes. This means that your ego will rarely get trampled.
Now, how to go about it:
a) Always begin with a greeting. Allow time for a response before you plunge into another sentence.
b) Gauge the person's openness to talk with you by their response to your greeting.
c) Avoid initiating a chat if the person is drunk or in the middle of something intense.
d) Safe ways to get started: make a comment about the weather, or ask a question.
a) Empieza con un saludo. Siempre. Deja que la otra persona pueda responder, antes de seguir adelante. Saludos comunes:
b) Puedes tantear la voluntad de la otra persona de platicar contigo, de acuerdo al saludo.
c) No trates de platicar con alguien si está borracho o si está metido en algo intenso.
d) Buenos temas para comenzar: comenta sobre el tiempo, o haz una pregunta, por ejemplo:
Por fin sale el sol, ¿eh?
¿Cree que va a llover hoy?
¿Por aquí hay un ... taller mecánico ... parada de autobús ... parque con juegos infantiles ... campo de futbol?