Staying in central L.A. would not help you to reach Six Flags since it is far from the center of L.A. The EASIEST and QUICKEST way to get to Universal and Six Flags from Rose Av is to hire a car.
While I completely understand your hesitation to drive, these 2 particular attractions are extremely easy to reach by car since the drive involves driving almost exclusively on freeways (motorways). You simply exit the freeway into the parking area of the attraction.
While driving on the freeway, you need do nothing but hold the steering wheel steady and press on the right-hand pedal. Easy!
You've complicated the transfer a little because you're staying in an area that is not next to one of our freeways but you can call an enterprise.com car hire office and they will send someone to pick up and your family and take them to their office so you can retrieve the car.
The nearest Enterprise office to Rose Av is the one at 2700 Lincoln Bl I picked a location on Rose Av that's in the center of Santa Monica. Here's a map of the route from such a location to the car hire lot:
It's a 4-minute ride.
When you pick up the car, here are the basic steps you'll take to reach these attractions:
1. For both attractions, you'll head north on Lincoln Bl (the street that the Enterprise office is on). The drive will only be .9 miles / 1.4 km (a 1 to 2 minute drive). Ahead, you'll see large signs for the Santa Monica Freeway aka Interstate 10 eastbound.
2. You'll turn right at the sign which will put you on Olympic Bl and you'll then bear left off of Olympic onto the freeway,
3. Now you're going to hold the wheel steady and drive for 2.7 miles / 4.2 km -- a 2 to 3 minute drive. You'll see large signs announcing the exits for the San Diego Freeway aka Interstate 405. You'll want to get onto the 405 northbound.
4. Now, it's time to hold the wheel steady again and compliment yourself on how good a job you're doing. The motorway will slope upwards into the Canyon. You'll reach the top and then it will head downward. The San Fernando Valley (our northern suburbs) will be displayed in the distance. You'll drive this for about 10 miles / 16 km and the ride will take about 10 minutes.
5. At the bottom of the hill, you'll see huge signs for the 101 freeway aka Ventura Freeway. Here is where your drive will vary based upon your eventual destination. But first, let's look at where you've driven thus far...
Here's a map of the route. Use the scroll bars to the left of the map to look at the turn-by-turn directions.
The important thing to note at this point is how long you've been driving. It's 17 minutes (could be longer if you drive in the morning 'rush hour' between 6:00 and 9:00). You're about 1/2 way there and, to be honest, if you used public transit or a tour, it would take more than twice as long -- each way!
Okay, so let's see what happens next.
a. If you're headed to Six Flags, when you reach the exit for the 101 freeway, you'll simply drive right past it and continue driving on the 405 freeway for about 10 miles / 16 km (about a 10 minute drive).
At this point, the 405 will come to an end and will merge into the 5 Freeway aka Golden State Freeway. So just keep driving. 11 miles / 17 km later (about 11 minutes of driving), you'll see the exit sign for Magic Mountain.
Let's look at this section of the route: http://mapq.st/WAkBXJ
So, that's 38 minutes, door-to-door! Fast and easy!
b. If you're heading to Universal, your route will vary from the Magic Mountain route. Starting on the 405 freeway as you approach the exit for the 101 freeway at the bottom of the hill...
Transfer onto the 101 freeway eastbound and drive the 7.4 miles / 12 km (7 minutes) to the exit for Universal Studios. Let's look at the complete route from the Enterprise office to Universal:
That's a 31 minute drive (more, with traffic).
Another advantage to driving is that you can come and go to the attractions on your own schedule and stop for dinner at any place you wish.