I can't speak to the safety of Hawthorne, though most tourist hotels in LA are in reasonably safe locations. It's not very central though, even assuming you're driving. It's close to LAX and close to Manhattan Beach, but 13-15 miles to Beverly Hills (depending on your route) and 17 miles to Universal Studios. There is likely to be serious traffic between the hotel and any Westside destinations, especially on the 405. You might want to look for a more central hotel.
I agree with Wanderer's comments. With a car this is not a very central, and without a car its largely unworkable. It actually is only about 1/4 mile walk to a station for the Green Line light rail train (www.metro.net), but the Green Line, as some locals like to say, is the train that "goes from nowhere to nowhere". It won't be of all that much use to you as a tourist (though you can use it in combination with the Blue Line and Red Lines to reach Universal Studios, but probably 90+ minutes each way), and bus access in this area isn't really very good to the touristy parts of the city without large numbers of transfers from bus to bus. To get from here to Beverly Hills via bus, for instance, is not something I'd want to contemplate. It would probably involve taking the green line to the Aviation Blvd. station, Big Blue Bus Rapid 3 from there to Santa Monica, and then from Santa Monica Metro Bus 704 to Beverly Hills. I'd have to check the times but this would likely also be 70-90 minutes each way.
By the way, to add two things - yes this area is safe - in particular its pretty nice to the west of the hotel along Rosecrans Ave. The 2nd thing is that one redeeming factor for this location is that there are a good selection of fast food and nicer restaurants on Rosecrans Ave. between Aviation Blvd. where the hotel is and Sepulveda Blvd. which is about a mile away.
Thanks everyone for the responses. I guess my real question is where can we stay that is centrally located in between LAX and Universal Studios? We want to be close enough to LAX to catch a flight in the morning but also plan on a day at Universal.
Did you choose the Springhill Suites because you want to stick with a Marriott brand hotel, or is the price what you are looking for, and what is your budget?
Being a few blocks from the freeway is helpful. Many people drive the 45 minutes to Universal, to be 10 minutes from LAX the next morning.