In my understanding (not a native speaker of English, obviously) “towards” means that the street goes in the direction of the center, possibly without reaching it. “To the center” means that it actually reaches the center.
I would translate “to the center” by “la centru” instead of “spre centru.” Of course the second does not exclude the first, as in English.
Maybe they should be. But they aren't. I know that problem from my own native language.
- A street is “a thoroughfare especially in a city, town, or village … that usually includes sidewalks” (Merriam-Webster)
- A road is “an open way for vehicles, persons, and animals” (Merriam-Webster)
I am not so sure about Romanian but I would roughly translate street by stradă and road by drum or maybe rută.