During June daylight last till a little past 7:00 PM. The only well lit area I can think of is the "Paseo de la Princesa". It's well lit, has vendors on the sidewalks and a beautifull fountain at the end. I wouldn't go past the fountain with a kid, it's not as well lit, and it's more like a romantic spot. I wouldn't recommend going to the San Cristobal fort after dark. It's near La Perla, not the safest neighborhood around.
If you do decide you need to see a fort, you can go to El Morro and see it from the outside, it's still impressive. Near the entrance is the big Totem pole. From El Morro you can just walk down the streets. From the Totem keep going down, and look for a restaurant in a corner, "El Patio de Sam" (Corder of San Sebastian and Del Cristo streets). Going down Calle del Cristo, you'll see Hotel El Convento to your right, and to your left The Old San Juan Cathedral (if there's a religious service, you're in luck otherwise it might be closed). At the next intersection, to the right will be the Fortaleza or Executive Mansion. Turn left into Calle de la Fortaleza, go down that street one, two or three blocks and turn right on any of those blocks (pick the most well lit one you see, or the one with the most people and traffic of pedestrians), the next street you'll run into will be Calle Tetuan. From there, keep going down, past Calle Recinto Sur, until you reach the water. Turn left until you reach your terminal.
I know Old San Juan might be a little intimidating to tourists at night, but it's actually a prominent social spot with the young, college age kids. The only problem for us "locals" is the traffic and where to park, but other than that, we enjoy it a heck of a lot.
If tourists excersice caution and stay aware of their surroundings, remain in well lit, high pedestrian traffic areas, you should be ok, ill intentioned people look for vulnerable people, those who look lost. And if you DO find yourself lost, ask around! There are plenty of establishments around (fast foods, bars) where you can find directions. Most people here in Puerto Rico are friendly and outgoing you just have to ask. Hint: Where's the dock is "Donde queda el muelle?", How do I get to the dock is "Como llego al muelle?" If they don't speak english, use gestures. It's not that hard to say 3 (points left) 1 (points down) (referring to blocks). =)
If you have any questions, feel free to email me. I'll answer to the best of my abilities.
Ana Marylee