We were just there last week and the traffic was awful. We stayed at DLR, and we moved to the Hilton up by Universal. We had moved from DLR to a hotel near Newport beach for 2 nights before Universal. We got lucky on our drive between Newport Beach and the Hilton and Universal and did not hit too much traffic and it only took about an hour.
Our arrival day at the Hilton we drove down to the Santa Monica Pier after checking in. It is only about 20 miles away, but the drive was an hour each way.
I would also expect it to be an hour each way from the Santa Monica pier to Warner Brothers. Warner Brothers is about the same distance from the Pier as the Universal area. Warner Brothers was only 3 miles and 10 minutes away from our hotel at Universal.
Depending on traffic, it could wind up taking 2 hours for you to get from the Santa Monica Pier to
Disneyland. It is about 45 miles. If there is not much traffic you are probably looking at about an hour. We drove from the Griffith Observatory to John Wayne Airport which is also about 45 miles on our departure day-- we left Observatory at 1:30 pm as we had a 5:15 flight, and it took us just over two hours to get to the airport. We didn't expect it to take that long as we weren't driving in rush hour.
How many days are you staying in the Santa Monica area? Have you thought about maybe moving hotels for some of your days to places closer to what you plan to do? We found the Santa Monica pier area a little rough for our tastes as opposed to the other areas where we have stayed in California (both beach and otherwise). I've heard the Shore hotel is really nice though.